Question

The endpoint of a line segment are X(1,7) and Y(-3,11). What is the length of XY?

Answer 1

The length of the line segment XY with endpoints X(1,7) and Y(-3,11) is approximately 5.66 units, calculated using the distance formula which incorporates the coordinates of both points.

Step-by-step explanation:

The length of the line segment XY with endpoints X(1,7) and Y(-3,11) can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula for two points X(x1, y1) and Y(x2, y2) is given by:

√((x2 - x1)^2 + (y2 - y1)^2)

Here, the coordinates for X and Y are (1, 7) and (-3, 11), respectively. Let's calculate the length step-by-step:

1. Substitute the coordinates into the formula: √((-3 - 1)^2 + (11 - 7)^2)
2. Simplify the differences: √((-4)^2 + (4)^2)
3. Calculate the squares: √(16 + 16)
4. Combine the terms: √(32)
5. Take the square root: Approx 5.66

The length of the line segment XY is approximately 5.66 units.