For what value of X are the points A (-3, 12), B (7, 6) and C (x, 9) collinear. Option 1: 3 Option 2: -3 Option 3: 2 Option 4: -2

Answer: 2. Solution: For collinearity, slope AB = slope BC. Slope AB = (6-12)/(7-(-3)) = (-6)/10 = -3/5. Slope BC = (9-6)/(x-7) = 3/(x-7). Setting equal: -3/5 = 3/(x-7) -3(x-7) = 15 x = 2.

Geometry

Miscellaneous

Medium

For what value of X are the points A (-3, 12), B (7, 6) and C (x, 9) collinear.

-3

-2

✅ Correct Option: 3

For collinearity, slope AB = slope BC. Slope AB $= \frac{6-12}{7-(-3)} = \frac{-6}{10} = -\frac{3}{5}$ .

Slope BC $= \frac{9-6}{x-7} = \frac{3}{x-7}$ . Setting equal: $-\frac{3}{5} = \frac{3}{x-7} \Rightarrow -3(x-7) = 15 \Rightarrow x = 2$ .

2026: 25 May Shift 1

Match the LIST-I with LIST-II

LIST-I (Geometrical Function)		LIST-II (Formula)
A. Area of a Triangle	I.	2 (Length + Breadth)
B. Perimeter of a Rectangle	II.	$\pi\times(\text{Radius})^2$
C. Area of a Parallelogram	III.	1/2 ( Base × Height)
D. Area of a Circle	IV.	Base × Height

Choose the correct answer from the options given below:

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For what value of X are the points A (-3, 12), B (7, 6) and C (x, 9) collinear.

Solution

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