Question

A line segment has a skid point of (3,502). If one endpoint is (6,2), what is the other endpoint?

a. (0,1002)
b. (9,1002)
c. (0,502)
d. (9,502)

Answer 1

The other endpoint of the line segment, given the midpoint (3,502) and one endpoint (6,2), is (0, 1002). This is found by using the midpoint formula and solving for the unknown coordinates.

Step-by-step explanation:

The question involves determining the other endpoint of a line segment if the midpoint (also referred to as the 'skid point' in the question) and one of the endpoints are known. To find the other endpoint of a line segment, you apply the midpoint formula, which is derived from the averages of the x-coordinates and the y-coordinates of the endpoints. In this case:

• Midpoint: (3, 502)
• Known endpoint: (6,2)

The midpoint is calculated as the average of the x-coordinates and the y-coordinates of the endpoints:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the known values we get:

(3, 502) = ((6 + x2) / 2, (2 + y2) / 2)

Solving the equations:

3 = (6 + x2) / 2
502 = (2 + y2) / 2

We find:

x2 = 2(3) - 6 = 0
y2 = 2(502) - 2 = 1002

So, the other endpoint of the line segment is (0, 1002).