Quadrilateral PAID is a rectangle whose diagonals have the endpoints P(-3, -2)I(4, -7) and A(4, -2)D(-3, -7). Find the diagonals' intersection point. In complete sentences, explain which method you used for finding the intersection point.
Accepted Solution
A:
Answer:The intersection point of diagonals is (0.5,-4.5).Step-by-step explanation:The end points of first diagonal are p(-3, -2) and i(4, -7).The end points of second diagonal are a(4, -2) and d(-3, -7).If a line passing through two points, then the equation of line is[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The equation of first diagonal is[tex]y-(-2)=\frac{-7-(-2)}{4-(-3)}(x-(-3))[/tex][tex]y+2=\frac{-5}{7}(x+3)[/tex][tex]7y+14=-5(x+3)[/tex][tex]7y+14=-5x-15[/tex][tex]5x+7y=-29[/tex] .... (1)The equation of second diagonal is[tex]y-(-2)=\frac{-7-(-2)}{-3-4}(x-4)[/tex][tex]y+2=\frac{-5}{-7}(x-4)[/tex][tex]7y+14=5(x-4)[/tex][tex]7y+14=5x-20[/tex][tex]5x-7y=34[/tex] .... (2)Add equation (1) and (2),[tex]10x=5[/tex][tex]x=0.5[/tex]Put this value in (1).[tex]5(0.5)+7y=-29[/tex][tex]y=-4.5[/tex]The intersection point of diagonals is (0.5,-4.5).