Triangle DFG has vertices D (2, 4), F (4, 8), and G (6, 4) Triangle DFG has vertices D (2, 4), F (4, 8), and G (6, 4). Triangle DFG is dilated by a scale factor of and has the origin as the center of dilation. What are the coordinates of F’? A B C D Problem #1 Obj 6 - TAKS 2004 9th [8.6(A)]

is shown below. Which scale factor was used to transform ? Problem #2 Obj 6 - TAKS 2004 9th [8.6(A)]

Triangle KLM has coordinates K(–8, 3), L(–4, 1), and M(–2, 7) Triangle KLM has coordinates K(–8, 3), L(–4, 1), and M(–2, 7). What will be the new coordinates of point M if the triangle is translated 4 units to the right and 3 units down? A (0, –2) B (2, 4) C (–4, 0) D (–6, 4) Problem #3 Obj 6 - TAKS 2004 9th [8.7(D)]

Triangle XYZ is translated so that X is mapped to X’. Which coordinate pair best represents Y’? A (–3, –8) B (2, –7) C (2, –6) D (2, –2) Problem #4 Obj 6 - TAKS 2004 9th [8.6(B)]

At what coordinates should vertex Z be placed to create a quadrilateral WXYZ that is similar to quadrilateral PQRS? A (24, 16) B (24, 24) C (20, 20) D (16, 24) Problem #5 Obj 6 - TAKS 2004 10th [8.6(B)]

If quadrilateral TUVW is reflected across the x-axis to become quadrilateral T’U’V’W’, what will be the coordinates of W’? A (–4, –2) B (–4, 2) C (2, –4) D (4, –2) Problem #6 Obj 6 - TAKS 2004 10th [8.6(B)]

A portion of isosceles trapezoid NPRT is shown on the grid to the right. At what coordinates should vertex T be place to make segment NP parallel to segment RT in order to complete isosceles trapezoid NPRT? A (–2, –2) B (–3, –2) C (–2, –3) D (–4, –5) Problem #7 Obj 6 - TAKS 2004 10th [8.7(D)]

Which point on the grid satisfies the conditions x ≥ 5 and y < –1? A W B X C Y D Z Problem #8 Obj 6 - TAKS 2004 10th [8.7(D)]

A copy machine can enlarge or reduce letters proportionally A copy machine can enlarge or reduce letters proportionally. Which would not be an enlargement or reduction of the letter to the right? Problem #9 Obj 6 - TAKS 2004 10th [8.6(A)]

Doris had a circular garden with a radius of 30 feet Doris had a circular garden with a radius of 30 feet. She used all of the fencing from the circular garden to enclose a square garden. The length of each side of Doris’s square garden was approximately: A 47 feet B 94 feet C 120 feet D 188 feet Problem #10 Obj 6 - TAKS 2004 11th [G.B4(A)]

Which pair of the following polygons is congruent? A Polygon A and Polygon C B Polygon B and Polygon D C Polygon A and Polygon B D Polygon B and Polygon C Problem #11 Obj 6 - TAKS 2004 11th [G.E3(A)]

About how high off the ground is kite? A kite string is 220 feet long from the kite to the ground. The string makes a 45° angle with the ground. About how high off the ground is kite? A 110 ft B 127 ft C 156 ft D 311 ft Problem #12 Obj 6 - TAKS 2004 11th [G.C1(C)]

Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is sewing a line of sequins from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of sequins be? A 13.4 in. B 10.4 in. C 8.5 in. D 5.2 in. Problem #13 Obj 6 - TAKS 2004 11th [G.C1(C)]

What is the measure of angle BAE in degrees? In the figure shown to the right, segment BC is parallel to segment ED, and segment AE is perpendicular to segment ED. The measure of angle ABC is 130°. What is the measure of angle BAE in degrees? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. Problem #14 Obj 6 - TAKS 2004 11th [G.C1(A)]

If the perimeter of this trapezoid is 32 units, what is its area? The lengths of the bases of an isosceles trapezoid are shown to the right. If the perimeter of this trapezoid is 32 units, what is its area? A 44 square units B 110 square units C 88 square units D 55 square units Problem #15 Obj 6 - TAKS 2004 11th [G.C1(C)]

Use the table to determine the expression that best represents the number of diagonals of any convex polygon having n sides. A B C D Problem #16 Obj 6 - TAKS 2004 11th [G.C1(A)]

Regular pentagon MNPQR is similar to pentagon TUVWX Regular pentagon MNPQR is similar to pentagon TUVWX. What scale factor was used to dilate regular pentagon MNPQR to pentagon TUVWX. A 0.4 B 1.8 C 2.5 D 4.2 Problem #17 Obj 6 - TAKS 2004 8th [8.6(A)]

If triangle XYZ is translated 8 units to the left and 3 units down, what are the coordinates of point Y’? A (9, 5) B (–2, 6) C (1, 2) D (–4, 2) Problem #18 Obj 6 - TAKS 2004 8th [8.6(B)]

A circle with a radius of 6 units is shown to the right A circle with a radius of 6 units is shown to the right. What are the coordinates of the center of the circle? A (–1, 2) B (–2, 3) C (–2, 2) D (–3, 2) Problem #19 Obj 6 - TAKS 2004 8th [8.7(D)]

Polygon PQRSTU is shown on the coordinate grid below. Problem #20 Obj 6 - TAKS 2003 8th [8.6(B)]

Which coordinate grid shows the reflection of polygon PQRSTU across the x-axis? Problem #20 Obj 6 - TAKS 2003 8th [8.6(B)]

Quadrilateral PQRS was dilated to form quadrilateral WXYZ. Which number best represents the scale factor used to change quadrilateral PQRS into quadrilateral WXYZ? A B C 2 D 4 Problem #21 Obj 6 - TAKS 2003 8th [8.6(A)]

A circle with a radius of 3 units has its center at (-4, -2) on a coordinate grid. If the circle is translated 6 units to the right and 3 units up, what will be the coordinates of the new center? A (2, 1) B (1, 2) C (–2, 1) D (1, –2) Problem #22 Obj 6 - TAKS 2003 8th [8.6(B)]

Which circle has a center located at coordinates (–3, 2)? Problem #23 Obj 6 - TAKS 2003 9th [8.6(B)]

The pentagon in the graph to the right is to be dilated by a scale factor of . Which graphs shows this transformation? Problem #24 Obj 6 - TAKS 2003 9th [8.6(A)]

Problem #24 Obj 6 - TAKS 2003 9th [8/6(A)]

Jake made a map of his neighborhood for a school project Jake made a map of his neighborhood for a school project. He placed a grid over the map. Which coordinate point best represents the post office? A. (6, 12) B. (12, 6) C. (1.2, 0.6) D. (0.6, 1.2) Problem #25 Obj 6 - TAKS 2003 9th [8.7(D)]

Triangle RST is shown on the coordinate plane below Triangle RST is shown on the coordinate plane below. Find the coordinates of the vertices of the image of triangle RST reflected across the y-axis? A. (–2, –3), (–4, –6), (–5, –1) B. (2, 3), (4, 6), (5, 1) C. (0, 3), (–2, 6), (–3, 1) D. (2, –3), (4, –6), (5, –1) Problem #26 Obj 6 - TAKS 2003 9th [8.6(B]

Identify the location of point P under translation (x + 3, y – 2). B. (2, 3) C. (–1, 0) D. (2, 0) Problem #27 Obj 6 - TAKS 2003 10th [8.6(B)]

Identify the drawing that shows Figure 1 under dilation to produce Figure 2, using center of dilation (0, 0) and a scale factor of . Problem #28 Obj 6 - TAKS 2003 10th [8.6(A)]

The graph below shows triangle XYZ and similar triangle X’Y’Z’. Problem #29 Obj 6 - TAKS 2003 10th [8.6(A)]

A. All the corresponding angles will increase by a multiple of 3. Which statement is true when transforming triangle XYZ to triangle X’Y’Z’? A. All the corresponding angles will increase by a multiple of 3. B. All the corresponding angles will increase by a scale factor of . C. All the corresponding sides are proportional, with a scale factor of 3. D. All the corresponding sides are proportional, with a scale factor of . Problem #29 Obj 6 - TAKS 2003 10th [8.6(A)]

For which point is and ? A. M B. N C. P D. Q Problem #30 Obj 6 - TAKS 2003 10th [8.7(D)]

Triangle RST is translated so that R is mapped to R’ Triangle RST is translated so that R is mapped to R’. Which set of ordered pairs best identifies points S’ and T’? A. S’(8, 3), T’(3, 8) B. S’(4, 3), T’(9, 8) C. S’(10, –1), T’(12, –9) D. S’(10, 3), T’(5, 4) Problem #31 Obj 6 - TAKS 2003 10th [8.6(B)]

What are the measures of the three angles of the garden? On the map below, First Avenue and Second Avenue are parallel. A city planner proposes to locate a small garden and park on the triangular island by the intersections of four streets shown. What are the measures of the three angles of the garden? A. 90°, 65°, 25° B. 90°, 50°, 40° C. 90°, 60°, 30° D. 130°, 40°, 10° Problem #32 Obj 6 - TAKS 2003 11th [G.C1(A)]

A fence around a square garden has a perimeter of 48 feet A fence around a square garden has a perimeter of 48 feet. Find the approximate length of the diagonal of this square garden. A. 12 feet B. 17 feet C. 21 feet D. 24 feet Problem #33 Obj 6 - TAKS 2003 11th [G.C1(C)]

If angle A and angle B are complementary angles and the measure of angle A is x, which equation can be used to find y, the measure of angle B? A. y = 90 + x B. y = 90 – x C. y = 180 – x D. y = x + 180 Problem #34 Obj 6 - TAKS 2003 11th [G.B4(A)]

A. Rotate figure MNPQ 90° around M Figure MNPQ is shown on the coordinate plane. Which transformation creates an image with a vertex at the origin? A. Rotate figure MNPQ 90° around M B. Reflect figure MNPQ across the line x = 1 C. Reflect figure MNPQ across the line y = 2.5 D. Translate figure MNPQ to the left 6 and down 5 Problem #35 Obj 6 - TAKS 2003 11th [G.E3(A)]

Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet Mr. Ryan is flying his single-engine plane at an altitude of 2400 feet. He sees a cornfield at an angle of depression of 30°. What is Mr. Ryan’s approximate horizontal distance from the cornfield at this point? A. 1200 feet B. 3394 feet C. 4157 feet D. 4800 feet Problem #36 Obj 6 - TAKS 2003 11th [G.C1(C)]

The figure below shows the first 3 stages of a fractal. How many circles will the nth stage of this fractal contain? A. 2n B. 2n C. 2n – 1 D. 2n – 1 Problem #37 Obj 6 - TAKS 2003 11th [G.C1(A)]

Find the equation that can be used to determine the total area of the composite figure shown below. Problem #38 Obj 6 - TAKS 2003 11th [G.B4(A)]

Points K and L are shown on the grid below. If point K is the midpoint of JL, what are the coordinates of endpoint J? F. (6, −5) G. (−6, 7) H. (0, 1) J. (−4, 5) Problem #39 Obj 6 - TAKS 2006 9th [8.7(D)]

Which scale factor was used to transform AHP to ENK? F. G. H. J. AHP ~ ENK as shown below. Which scale factor was used to transform AHP to ENK? F. G. H. J. Problem #40 Obj 6 - TAKS 2006 9th [8.6(A)]

A. Point K B. Point M C. Point R D. Point U Which point on the grid below best represents the coordinates , ? A. Point K B. Point M C. Point R D. Point U 8 3 7 Problem #41 Obj 6 - TAKS 2006 9th [8.7(D)]

LMN has vertices L (a, b), M (r, s), and N (u, v). What will be the new coordinates of point M if the triangle is translated 7 units to the right and 3 units down? F. (r + 3, s − 7) G. (r + 7, s − 3) H. (r − 7, s + 3) J. (r − 3, s + 7) Problem #42 Obj 6 - TAKS 2006 9th [8.6(B)]

KQR is translated so that R is mapped to R . Which ordered pair best represents either point K or point Q ? F. K (−3, 6) G. Q (−4, −1) H. K (5, −2) J. Q (−3, −2) Problem #43 Obj 6 - TAKS 2006 10th [8.6(B)]

Which of the following ordered pairs best represents the location of point T? Problem #44 Obj 6 - TAKS 2006 10th [8.7(D)]

Pentagon PQRST is graphed on the coordinate grid below. Which of the following points would be the location of S if pentagon PQRST is dilated by a scale factor of 2 and has a center of dilation at (0, 0)? (−6, 4) G. (2, −6) H. (4, −6) J. (4, −3) Problem #45 Obj 6 - TAKS 2006 10th [8.6(B)]

Look at the cylinder shown below. Which of the following cylinders is similar to the one above? Problem #46 Obj 6 - TAKS 2006 10th [8.6(A)]

Problem #46 Obj 6 - TAKS 2006 10th [8.6(A)]

The circle shown below has a diameter of 10 units. Which of the following ordered pairs best represents the location of the center of the circle? F. (−2, ) G. (−2, 4) H. (−2, ) J. (−2, ) Problem #47 Obj 6 - TAKS 2006 10th [8.7(D)]

The first 4 stages of a certain fractal are shown below. In each stage after the first, each square is divided into 4 squares, and then the bottom right square is removed. If the pattern continues, how many shaded square units will Stage 5 contain? F. 243 G. 54 H. 81 J. 27 Problem #48 Obj 6 - TAKS 2006 11th [G.C1(B)]

Which is closest to the length of the hose in the garden? A. 7.8 ft Mr. Schultz has a garden shaped like an equilateral triangle that measures 11 feet on each side. He has placed a watering hose that extends from the faucet located at a vertex to the opposite side, as shown below. Which is closest to the length of the hose in the garden? A. 7.8 ft B. 9.5 ft C. 6.4 ft D. 5.5 ft Problem #49 Obj 6 - TAKS 2006 11th [G.C1(C)]

Look at the cube shown below. Which equation best represents the area of the shaded rectangle located diagonally in the cube? A. A = C. A = B. A = D. A = Problem #50 Obj 6 - TAKS 2006 11th [G.B4(A)]

Look at the figure shown below. Which expression does not represent the area of the figure? A. bc − ef B. af + ad − de C. de + af + ad D. af + cd Problem #51 Obj 6 - TAKS 2006 11th [G.B4(A)]

Parallelogram WBMP is shown on the grid below. If WBMP is reflected across the line y = −x and then translated 4 units down to become parallelogram W B M P , what will be the coordinates of M ? F. (−6, −7) G. (6, −1) H. (6, 7) J. (6, 3) Problem #52 Obj 6 - TAKS 2006 11th [G.E3(A)]

water surface and the water depth? The figure below shows a conical cup containing water. The water depth can be represented by x, and the area of the water surface can be represented by A. As the water depth changes, the area of the water surface changes, as shown in the table below. Which equation best represents the relationship between the area of the water surface and the water depth? Problem #53 Obj 6 - TAKS 2006 11th [G.C1(A)]

F. A = G. A = H. A = J. A = Problem #53 Obj 6 - TAKS 2006 11th [G.C1(A)]

In the figure shown below, MN = 10 centimeters. Which is closest to the length of TN? A. 7 cm B. 6 cm C. 17 cm D. 14 cm Problem #54 Obj 6 - TAKS 2006 11th [G.C1(C)]