Question

If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?

Answer 1

The question is incomplete. Here is the complete question.

If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?

B(1, 3) and D(1, −2)

B(3, 3) and D(3, −2)

B(2, 3) and D(2, −2)

B(1, 2) and D(1, −3)

Answer: B(1, 3) and D(1, -2)

Step-by-step explanation: Area of a rectangle is the multiplication of its width and its length.

The rectangle to be has length, or distance from point A to point C, of 5 units.

For the area to be 20, width has to be 4.

Point B will be 4 units to the right of point A, which means:

$x_{B}=x_{A}+4$

Point A has coordinates ( -3, 3), then:

$x_{B}=-3+4$

$x_{B}=1$

Because the points is "moved" to the right, instead of up or down, y-coordinate stays the same:

$y_{B}=y_{A}$

$y_{B}=3$

Point D will be 4 units to the right of point C:

$x_{D}=x_{C}+4$

Coordinates of point C are ( -3, -2):

$x_{D}=-3+4$

$x_{D}=1$

Because a rectangle has a pair of sides parallel to each other, D's y-coordinate will also be the same:

$y_{D}=y_{C}$

$y_{D}=-2$

Coordinates of points B and D that makes rectangle ABCD have area of 20 square units are (1, 3) and (1, -2), respectively.