Report

1.6 Midpoint and Distance in the Coordinate Plane Midpoint and Distance • Coordinate Plane- a plane divided into four regions by an x-axis and y-axis • Midpoint Formula: x1 x2 y1 y2 M , 2 2 Practice Problems: 1)Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). 2)Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3). Practice Problems: 3)M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. 4)S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T. Distance Formula • Distance Formula: d ( x2 x1 ) ( y2 y1 ) 2 2 Practice Problems: 5) Find FG and JK. Then determine whether FG JK. F(1, 2) G(5, 5) J(-4, 0) K(-1, -3) Practice Problems 6) Find EF and GH. Then determine if EF GH. E(-2, 1) G(-1, -2) F(-5, 5) H(3, 1) Right Triangles leg • Parts of a right triangle: leg Pythagorean Theorem • For right triangles: the sum of the squares of the length of the legs is equal to the square of the length of the hypotenuse a b c 2 2 2 Practice Problems: 7) Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5).