Question

What is the perimeter of △CDE?
C=(-3,7)
D=(9,7)
E=(9,2)
Perimeter = _____ units

Answer 1

To find the perimeter of triangle \( \triangle CDE \), we need to calculate the lengths of the three sides \( CD \), \( DE \), and \( EC \).

1. **Calculate \( CD \)**:
- Points \( C(-3, 7) \) and \( D(9, 7) \) lie on the same horizontal line because they have the same y-coordinate.
- The length \( CD \) is the difference in the x-coordinates:
\[
CD = |x_D - x_C| = |9 - (-3)| = |9 + 3| = 12 \text{ units}
\]

2. **Calculate \( DE \)**:
- Points \( D(9, 7) \) and \( E(9, 2) \) lie on the same vertical line because they have the same x-coordinate.
- The length \( DE \) is the difference in the y-coordinates:
\[
DE = |y_E - y_D| = |2 - 7| = 5 \text{ units}
\]

3. **Calculate \( EC \)**:
- Points \( E(9, 2) \) and \( C(-3, 7) \) are not aligned with the coordinate axes, so we use the distance formula:
\[
EC = \sqrt{(x_C - x_E)^2 + (y_C - y_E)^2} = \sqrt{(-3 - 9)^2 + (7 - 2)^2}
\]
\[
EC = \sqrt{(-12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ units}
\]

4. **Calculate the perimeter**:
- Now we sum the lengths of all three sides:
\[
\text{Perimeter} = CD + DE + EC = 12 + 5 + 13 = 30 \text{ units}
\]

Thus, the perimeter of \( \triangle CDE \) is \( \boxed{30} \) units.