Question

What is the perimeter of rectangle HIJK?
I = (2,2)
J = (6,2)
K = (6,-7)
H = (2,-7)
Perimeter = ______ Units

Answer 1

To find the perimeter of rectangle HIJK, we first need to determine the lengths of its sides.

The coordinates of the vertices are:
- \( I = (2, 2) \)
- \( J = (6, 2) \)
- \( K = (6, -7) \)
- \( H = (2, -7) \)

Now we can calculate the lengths of the sides:

1. **Length of side IJ:**
\[
IJ = x_J - x_I = 6 - 2 = 4 \text{ units}
\]

2. **Length of side IH (or JK):**
\[
IH = y_I - y_H = 2 - (-7) = 2 + 7 = 9 \text{ units}
\]

The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (\text{Length} + \text{Width})
\]
In this case, the Length is 4 units, and the Width is 9 units.

Now let's calculate the perimeter:
\[
P = 2 \times (4 + 9) = 2 \times 13 = 26 \text{ units}
\]

Thus, the perimeter of rectangle HIJK is \( \boxed{26} \) units.