Find the perimeter of rectangle EFGH, with vertices E(−3,9), F(1,9), G(1,−5), and H(−3,−5)
To find the perimeter of rectangle EFGH, we need to add up the lengths of all four sides.
The distance between points E and F can be found using the distance formula:
d = √[(1 - (-3))^2 + (9 - 9)^2]
d = √[4^2 + 0^2]
d = √16
d = 4
Similarly, the distance between points F and G can be found:
d = √[(1 - 1)^2 + (-5 - 9)^2]
d = √[0^2 + 14^2]
d = √196
d = 14
The distance between points G and H is also 4, as G and H have the same y-coordinate.
Finally, the distance between points H and E can be found:
d = √[(-3 - (-3))^2 + (-5 - 9)^2]
d = √[0^2 + 14^2]
d = √196
d = 14
Now we can add up the lengths of all four sides:
Perimeter = 4 + 14 + 4 + 14
Perimeter = 36
Therefore, the perimeter of rectangle EFGH is 36.