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Sec 1-3 Concept: Use Midpoint and Distance Formulas Objective: Given coordinates in a plane, find lengths of segments as measured by a s.g.

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**Example 1: Find the length of AB**

One way would be to use the Pythagorean Thm. a2+b2=c2 X Y A B C C 3 32+42=C2 9+16 = C2 25=C2 √25 = √C2 5 = C 4

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Distance Formula: A B (x2,y2) C C2 = a2+b2 y2-y1 (x2,y1) (x1,y1) x2-x1

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Distance Formula If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the distance between A and B is

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**Example 2: Use the distance formula to find the length of AB**

Y A B (6,4) (2,1) AB = 5

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**Example 3: Find the length of the segment with end points A(3,-2) and B(-4,1)**

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**Midpoint of a Segment: a point that divides the segment into 2 congruent segments (the middle)**

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**Example 4: Find the midpoint of DE with endpoints D(3,5) and E(-4,0)**

B. Find the midpoint of DE with endpoints D(-1,8) and E(2,-5)

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Example 5: The midpoint of XY is M(2,1). One endpoint is Y(-7,11). Find the coordinates of the other endpoint B. The midpoint of XY is M(-7,8). One endpoint is Y(4,-6). Find the coordinates of the other endpoint

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TODAY’S WORK

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Distance, Midpoint, & Slope. The Distance Formula Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2, y 2 = 1 d = Example:

Distance, Midpoint, & Slope. The Distance Formula Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2, y 2 = 1 d = Example:

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