Question

if one corner is -6,3 -3,4 -6,8 8,4 what is the length of the diagonal in the rectangle

Answer 1

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

Given the coordinates of the corners: (−6, 3), (−3, 4), (−6, 8), and (8, 4), we can calculate the length of the diagonal.

First, we need to find the length of one side of the rectangle by calculating the distance between two adjacent corners. Let's take the two corners: (−6, 3) and (−3, 4).

Using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

We have:

d = √((-3 - (-6))^2 + (4 - 3)^2)
= √((3)^2 + (1)^2)
= √(9 + 1)
= √10

Therefore, the length of one side of the rectangle is √10.

Since we know that the rectangle has opposite sides of equal length, we can use the Pythagorean theorem to find the length of the diagonal.

Using the Pythagorean theorem:

d^2 = a^2 + b^2

In this case, a and b are the lengths of the sides of the rectangle, which are both √10.

Therefore:

d^2 = (√10)^2 + (√10)^2
= 10 + 10
= 20

Taking the square root of both sides:

d = √20
= 2√5

Therefore, the length of the diagonal in the rectangle is 2√5.