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

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

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=(y_2-y_1)/(x_2-x_1)(x-x_1)`

The equation of first diagonal is

`y-(-2)=(-7-(-2))/(4-(-3))(x-(-3))`

`y+2=(-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)=(-7-(-2))/(-3-4)(x-4)`

`y+2=(-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).