Question

Use the image to answer the question.

A graph shows four quadrants with the x-axis and y-axis both ranging from negative 10 to positive 10 in increments of 1. Unlabeled points are plotted at left parenthesis negative 6 comma 8 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 4 comma negative 3 right parenthesis, and left parenthesis negative 6 comma negative 3 right parenthesis. A straight line joins the four points forming a rectangle.

What is the length of the diagonal of the rectangle? Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the length of the diagonal of the rectangle, we can use the distance formula.

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

We can calculate the distance between the points (-6, 8) and (4, 8):

d1 = sqrt((4 - (-6))^2 + (8 - 8)^2)
= sqrt(10^2 + 0^2)
= sqrt(100)
= 10

Next, we can calculate the distance between the points (4, 8) and (4, -3):

d2 = sqrt((4 - 4)^2 + (-3 - 8)^2)
= sqrt(0^2 + (-11)^2)
= sqrt(121)
= 11

Now, we can calculate the distance between the points (4, -3) and (-6, -3):

d3 = sqrt((-6 - 4)^2 + (-3 - (-3))^2)
= sqrt((-10)^2 + 0^2)
= sqrt(100)
= 10

Finally, we can calculate the distance between the points (-6, -3) and (-6, 8):

d4 = sqrt((-6 - (-6))^2 + (8 - (-3))^2)
= sqrt(0^2 + 11^2)
= sqrt(121)
= 11

Therefore, the length of the diagonal of the rectangle is the sum of these four distances:

diagonal = d1 + d2 + d3 + d4
= 10 + 11 + 10 + 11
= 42

Rounded to the nearest hundredth, the length of the diagonal is 42.00.