The vertices of a quadrilateral are a(-1, 6), b(-2, 4), c(2, 2), and d(3, 4). write a paragraph proof to determine whether quadrilateral abcd is a rectangle.

I am given that the vertices of quadrilateral ABCD are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). The slope formula applied to each pair of adjacent vertices gives the slopes (m) of the sides:

Because line segments with equal slopes are parallel, segment AB is parallel to segment CD and segment BC is parallel to segment DA.

Multiplying the slopes of one pair of adjacent sides, I find that .

If the product of the slopes of two segments is -1, then they are perpendicular. Since both pairs of opposite sides have been proven parallel, proving one pair of adjacent sides perpendicular implies that the other pair of adjacent sides are also perpendicular. Therefore, by definition, quadrilateral ABCD is a rectangle.

Step-by-step explanation:

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared