Question

What is the length of segment XY?

On a coordinate plane, line X Y has points (negative 4, 0) and (3, 2).
4.5 units
StartRoot 45 EndRoot units
StartRoot 53 EndRoot units
9 units

Answer 1

To find the length of segment XY, we can use the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given the points \(X(-4, 0)\) and \(Y(3, 2)\):

- \(x_1 = -4\), \(y_1 = 0\)
- \(x_2 = 3\), \(y_2 = 2\)

Now we can plug these coordinates into the distance formula:

\[
d = \sqrt{(3 - (-4))^2 + (2 - 0)^2}
\]

Calculating each part:

1. \(3 - (-4) = 3 + 4 = 7\)
2. \(2 - 0 = 2\)

Now substitute those values back into the formula:

\[
d = \sqrt{(7)^2 + (2)^2} = \sqrt{49 + 4} = \sqrt{53}
\]

Thus, the length of segment XY is \(\sqrt{53}\) units. Therefore, the answer is:

\(\sqrt{53}\) units.