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?
Answers
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:
[tex]x_{B}=x_{A}+4[/tex]
Point A has coordinates ( -3, 3), then:
[tex]x_{B}=-3+4[/tex]
[tex]x_{B}=1[/tex]
Because the points is "moved" to the right, instead of up or down, y-coordinate stays the same:
[tex]y_{B}=y_{A}[/tex]
[tex]y_{B}=3[/tex]
Point D will be 4 units to the right of point C:
[tex]x_{D}=x_{C}+4[/tex]
Coordinates of point C are ( -3, -2):
[tex]x_{D}=-3+4[/tex]
[tex]x_{D}=1[/tex]
Because a rectangle has a pair of sides parallel to each other, D's y-coordinate will also be the same:
[tex]y_{D}=y_{C}[/tex]
[tex]y_{D}=-2[/tex]
Coordinates of points B and D that makes rectangle ABCD have area of 20 square units are (1, 3) and (1, -2), respectively.
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