Presentation on theme: "Midpoints of line segments. Key concepts Line continue infinitely in both directions, their length cannot be measured. A Line Segment is a part of."— Presentation transcript:
Key concepts Line continue infinitely in both directions, their length cannot be measured. A Line Segment is a part of line that is noted by two end points (x 1, y 1 ) and (x 2, y 2 ). The length of a lie segment can be found using the distance formula.
Proving Midpoints You can prove that the midpoint is halfway between the endpoints by calculating the distance from each endpoint to the midpoint.
EXAMPLE Calculate the midpoint of the line segment with endpoints of (-2,1) and (4,10). First determine the endpoints of the line segment (in this case the points given) Second, substitute the values of (x 1, y 1 ) and (x 2, y 2 ) into the midpoint formula
Multiply the difference by the given ratio (1/4) (16)(1/4) = 4
The y value is down from the original endpoint, therefore subtract the product from the y-value of the endpoint. 7-4 = 3 The point that is ¼ the distance from the endpoint (-3,7) of the segment (-3,7) and (5,-9) is (-1,3)
Now you try: Determine the point that is 2/3 the distance from the endpoint (2,9) Of the segment with endpoints (2,9) and (-4,-6)
Find an endpoint A line segment has one endpoint at (12,0) and a midpoint (10, -2). Locate the second endpoint.
Analyze problem One endpoint is (12,0) Midpoint is (10,-2) The other endpoint is unknown
The endpoint of the segment with one endpoint at (12,0) and a midpoint at (10, -2) is (8, -4)
Calculate area of a triangle 1. find the equation of the line that represents the base of the triangle. 2. Find the equation of the line that represents the height of the triangle. 3.Find the point of intersection of the line representing the height and the line representing the base.
4. Calculate the length of the base of the triangle (distance formula). 5. Calculate the height of the triangle (distance formula). o 6. Calculate the area using the formula: o A = ½ bh
Guided example triangle with vertices A(1, -1) B(4,3) C(5, -3) Let AC be the base. Slope for this line is: M=(-3)-(-1) = -2 = -1 (5)-(1) 4 2
Write the equation for AC y – y 1 = m(x-x 1 ) point slope form Substitute -1/2 for m, and (1, -1) for (x 1, y 1 ) Y –(-1) = -1/2(X – 1) Simplify Y + 1 = -1/2x + ½ Isolate y: y = -1/2x -1/2