Question

10. Determine the most precise name for the quadrilateral & find the area. (2 points)

A(3,4) B(8,1) C(2,-9) D(-3,-6)

Answer 1

Rectangle is the most precise name for the quadrilateral and amp

Answer 2

Rectangle

Explanation:

Slope of line = change in y ÷ change in x

Slope of line AB =
`(1-4)/(8-3)=-\frac35`

Slope of line BC =
`(-9-1)/(2-8)=\frac53`

Slope of line DC =
`(-9+6)/(2+3)=-\frac35`

Slope of line AD =
`(-6-4)/(-3-3)=\frac53`

As slope of AB = slope of DC ⇒ AB is parallel to DC

As slope of BC = slope of AD ⇒ BC is parallel to AD

As the slope of AB (and DC) is perpendicular to BC (AD) then all interior angles = 90°

Therefore, quadrilateral is a rectangle.