Question

A quadilateral has diagonals represented by y=2x+5 and x+2y= -8. What is true about the quadrilateral? Please explain.

(Please do not give out a flat out answer without explaining, spam, or lie. I really want to understand this topic. Thank you!)

Answer 1

Answer:

The quadrilateral has diagonals which are perpendicular to each other.

Step-by-step explanation:

The equations of the diagonals are given, as

$y = 2x+5$  and  $x = 2y -8$.

The second equation can be written as,

$y = \frac{-x-8}{2} = \frac{-x}{2}-4$

The slope of the first line is m1 = 2 and slope of second line is m2 = $\frac{-1}{2}$.

Multiplying the two slopes, we get,

= (m1)(m2) = $(2)(\frac{-1}{2}) = -1$

In coordinate geometry, when slopes of two lines are perpendicular, their slopes product is -1.

Thus, above two lines are perpendicular.

Thus the quadrilateral can be Rhombus,Square or Kite.