Question

If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (D)

5

Answer 2

For collinear points, the slope between any two pairs of points must be equal. We set the slope of the line segment connecting (3, -2) and (x, 2) equal to the slope of the line segment connecting (x, 2) and (8, 8). This gives the equation $\frac{2 - (-2)}{x - 3} = \frac{8 - 2}{8 - x}$, which simplifies to $\frac{4}{x - 3} = \frac{6}{8 - x}$. Solving this linear equation yields $x=5$.