Question

Find the perimeter of rectangle ABCD , with vertices A(1,7) , B(4,7) , C(4,−4) , and D(1,−4) .(1 point) Responses 12 units 12 units 28 units 28 units 16 units 16 units 33 units

Answer 1

To find the perimeter of rectangle ABCD with the vertices A(1, 7), B(4, 7), C(4, -4), and D(1, -4), we first need to determine the lengths of the sides of the rectangle.

The length of side AB (the distance between points A and B) can be calculated using the formula for the distance between two points:
\[
\text{Distance} = |x_2 - x_1|
\]
For points A(1, 7) and B(4, 7):
\[
AB = |4 - 1| = 3 \text{ units}
\]

Next, we calculate the length of side AD (the distance between points A and D). Since A and D have the same x-coordinate (1), we use the y-coordinates to find the distance:
\[
AD = |7 - (-4)| = |7 + 4| = 11 \text{ units}
\]

Next, we find the perimeter of the rectangle using the formula:
\[
\text{Perimeter} = 2(\text{length} + \text{width}) = 2(AB + AD)
\]
Substituting the values we found:
\[
\text{Perimeter} = 2(3 + 11) = 2(14) = 28 \text{ units}
\]

Thus, the perimeter of rectangle ABCD is **28 units**.