Question

A polygon has the following coordinates: A(3,1), B(5,3), C(2,5), D(-1,5), E(-4,3), F(-2,1). Find the length of DC.

Answer 1

To find the length of a line given two points, we are going to use the distance formula, which is defined below:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

($(x_1, y_1)$ and $(x_2, y_2)$ are the two points)

The points in this problem are (2, 5) and (-1, 5). We can find the distance of DC by substituting these values into the distance formula and simplifying, as shown below:

$D = \sqrt{(-1 - 2)^2 + (5 - 5)^2$

• Substitute values into formula

$D = \sqrt{(-3)^2}$

• Combine like terms and then simplify $0^2$ to 0

$D = \sqrt{9}$

• Compute $(-3)^2 = 9$

$D = 3$

• Compute $\sqrt{9} = 3$

The length of DC is 3.