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1-6: Midpoint and Distance

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1 1-6: Midpoint and Distance
OBJECTIVES: Develop and apply the formula for midpoint. Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.

2 1-6: Midpoint and Distance
The two sides that form the right angle. Legs of Right Triangle The longest side of a right triangle. It’s across from the right angle. Hypotenuse of Right Triangle

3 1-6: Midpoint and Distance
Finding the midpoint of a segment: Take the average of the x-coordinates and the average of the y-coordinates of the endpoints. M B A

4 1-6: Midpoint and Distance
EXAMPLE 1: Find the coordinates of the midpoint of with endpoints and

5 1-6: Midpoint and Distance
EXAMPLE 2: M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.

6 1-6: Midpoint and Distance
You Try It! S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.

7 1-6: Midpoint and Distance
In a coordinate plane, the distance d between two points and Distance Formula In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Pythagorean Theorem

8 1-6: Midpoint and Distance
Example 3: Find FG and JK, then determine whether

9 Assignment p. 47: 1-9, 14, 15


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