Question

Point A, B, C are collinear and AB:AC = 1/4. Point A is located at (-3,8), point b is located at (x,y) and point c is located at (-3,-2). What are the values of x and y?

A) x=−3,y=−2
B) x=−6,y=−4
C) x=0,y=2
D) x=3,y=6

Answer 1

To find the values of x and y, we can set up the equation (x + 3) / (y - 8) = 1/4. Simplifying and solving for x and y gives x = -3 and y = -2.

Step-by-step explanation:

Given that point A, B, C are collinear and AB:AC = 1/4. We are given that point A is located at (-3,8), point B is located at (x,y) and point C is located at (-3,-2).

To find the values of x and y, we can use the concept of ratio. Since AB:AC = 1/4, we can set up the following equation:

(x - (-3)) / (y - 8) = 1/4

Simplifying the equation, we get:

(x + 3) / (y - 8) = 1/4

Cross multiplying, we get:

4(x + 3) = (y - 8)

Expanding the equation, we get:

4x + 12 = y - 8

Subtracting y from both sides, we get:

4x + 12 - y = - 8

Bringing all the terms to one side, we get:

4x - y = -20

Therefore, the values of x and y are x = -3 and y = -2.