Question

In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Answer 1

A

Explanation:

Since they lie on the same line, it means that they are collinear.

Since they are collinear, the value of the slope between each 2 point is the same. Hence, we can have points PQR with the slopes PQ, PR and QR being the same.

The general formula for finding the slope of a line with 2 end points is :

m = (y2 - y1)/(x2 - x1)

using the first two points,

m = (0 - 9)/-1 -2 = -9/-3 = 3

Now to get the value of n. We can use the second point and the point containing n.

This means:

3 = (21 - 0)/(n + 1)

3 = 21/n + 1

3n + 3 = 21

3n = 18

n = 6