Question

:

A coordinate plane with a point A at negative 3, 3 and C at negative 3, negative 2.
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? (4 points)


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 1

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

Option 1 is correct.

Explanation:

A coordinate plane with a point A at (-3,3) and C at (-3,-2)

If the area of the rectangle to be drawn is 20 square units.

Area of rectangle = Length × width

A and C are the coordinates of a rectangle. There should be two more point B and D.

We are given both B and D located right of points A and C.

Therefore, One side of rectangle should be AC

Distance formula of two point,
`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Length of rectangle, AC
`=√((-3+3)^2+(3+2)^2)=5`

Let us consider width of rectangle be CD

Area of rectangle = AC × CD

20 = 5 × CD

CD = 4

D is right of C, if shift point C 4 unit right to get point D

Now, shift C(-3,-2) 4 unit right

Point D = (-3+4,-2) = (1,-2)

Similarly if shift point A 4 unit right to get point B

Now, shift A(-3,3) 4 unit right

Point B = (-3+4,3) = (1,3)

Hence, B(1,3) and D(1,-2) another coordinate of rectangle.

Answer 2

B (1 , 3) , D (1 , -2)

Explanation:

∵ A (-3 , 3) , C (-3 , -2)

∵ They have the same x-coordinate

∴ AC is a vertical segment its length = 3 - -2 = 5

∵ The area of the rectangle = 20

∴ The width of it = 20 ÷ 5 = 4

∴ x-coordinate of B: -3 + 4 = 1

∴ y-coordinate of B : 3 ⇒ AB horizontal segment

∴ B (1 , 3)

∵ x-coordinate of BD is 1 ⇒ BD is vertical segment

∵ y-coordinate = 3 - 5 = -2

∴ D (1 , -2)