Question

For the line segment whose endpoints are X(1,2) and Y (6, 7), find the x coordinate for the point located 1/3 the distance from X to Y.

A. 3.5
B. 3.3
C. 2.7
D. 2.4

Answer 1

To find the x-coordinate of a point located 1/3 the distance from X to Y, use the formula x = x1 + t(x2 - x1) with the given values, resulting in an x-coordinate of approximately 2.7.

Step-by-step explanation:

The goal is to find the x-coordinate of the point that is 1/3 of the way from point X(1,2) to point Y(6,7). To find this, we will use the formula to find points on a line segment: x = x1 + t(x2 - x1), where x1 and x2 are the x-coordinates of the endpoints, and t is the fraction of the distance along the segment from point X to Y.

In this case, x1 = 1, x2 = 6, and t = 1/3. Substituting these values into the formula, we get:
x = 1 + (1/3)(6 - 1)

x = 1 + (1/3)(5)

x = 1 + 5/3

x = 1 + 1.666...

x = 2.666...

Therefore, the x-coordinate for the point located 1/3 the distance from X to Y is approximately 2.7, which corresponds to option C.