Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2, 1),A(−2,1),A, left parenthesis, minus, 2, comma, 1, right parenthesis, comma B(3, 1)B(3,1)B, left parenthesis, 3, comma, 1, right parenthesis, C(3, 4)C(3,4)C, left parenthesis, 3, comma, 4, right parenthesis, and D(-2, 4)D(−2,4)D, left parenthesis, minus, 2, comma, 4, right parenthesis.
What is the perimeter of rectangle ABCDABCDA, B, C, D?
Answers
Answer:
its 16
Step-by-step explanation:
Side ABABA, B had a length of 555 units.
Side DCDCD, C is opposite of side ABABA, B, so it also has a length of 555 units.
Since A(\greenD{-2},\blueD{1})A(−2,1)A, left parenthesis, start color #1fab54, minus, 2, end color #1fab54, comma, start color #11accd, 1, end color #11accd, right parenthesis and D(\greenD{-2}, \blueD{4})D(−2,4)D, left parenthesis, start color #1fab54, minus, 2, end color #1fab54, comma, start color #11accd, 4, end color #11accd, right parenthesis have the same \greenD{x}xstart color #1fab54, x, end color #1fab54-coordinates, they form a vertical line segment. Therefore the length of ADADA, D is the distance between the \blueD{y}ystart color #11accd, y, end color #11accd-coordinates:
\qquad \begin{aligned}\blueD{4}-\blueD{1}&=3\end{aligned}
4−1
=3
Side ADADA, D had a length of 333 units.
Side BCBCB, C is opposite of side ADADA, D, so it also has a length of 333 units
Now we can find the perimeter.
Perimeter is the sum of all the side lengths.
\begin{aligned} \text{Perimeter} &= 5+5+3+3 \\\\ \phantom{\text{Perimeter}}&= 16 \end{aligned}
Perimeter
Perimeter
=5+5+3+3
=16