Question

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

Answer 1

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of first diagonal is

$y-(-2)=\frac{-7-(-2)}{4-(-3)}(x-(-3))$

$y+2=\frac{-5}{7}(x+3)$

$7y+14=-5(x+3)$

$7y+14=-5x-15$

$5x+7y=-29$                         .... (1)

The equation of second diagonal is

$y-(-2)=\frac{-7-(-2)}{-3-4}(x-4)$

$y+2=\frac{-5}{-7}(x-4)$

$7y+14=5(x-4)$

$7y+14=5x-20$

$5x-7y=34$                         .... (2)

Add equation (1) and (2),

$10x=5$

$x=0.5$

Put this value in (1).

$5(0.5)+7y=-29$

$y=-4.5$

The intersection point of diagonals is (0.5,-4.5).