Midpoint And Distance in the Coordinate Plane Lesson 2

Example 1: Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). = (–5, 5)

Example 2: M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. Step 1 Let the coordinates of Y equal (x, y). Step 3 Find the x-coordinate. Set the coordinates equal. Multiply both sides by 2. The coordinates of Y are (10, –5). 12 = 2 + x 2 = 7 + y Simplify. – 7 –7 –5 = y – 2 –2 10 = x Subtract. Simplify.

You can use the Pythagorean Theorem to find the distance between two points in a coordinate plane. In a right triangle, the two sides that form the right angle are the legs. The side across from the right angle that stretches from one leg to the other is the hypotenuse. In the diagram, a and b are the lengths of the shorter sides, or legs, of the right triangle. The longest side is called the hypotenuse and has length c.

The Ruler Postulate can be used to find the distance between two points on a number line. The Distance Formula is used to calculate the distance between two points in a coordinate plane.

Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5). Method 2 Use the Pythagorean Theorem. Count the units for sides a and b. a = 5 and b = 9. c2 = a2 + b2 = 52 + 92 = 25 + 81 = 106 c = 10.3

Method 1 Use the Distance Formula. Substitute the values for the coordinates of D and E into the Distance Formula.