Q. If the points (1, x), (5, 2) and (9, 5) are collinear, the value of x is
(A) -5/2
(B) 1
(C) 5/2
(D) -1
Question from UPPSC Prelims CSAT 2024
Correct Answer: (D) -1
Explanation:
To determine the value of x that makes the points (1, x), (5, 2), and (9, 5) collinear, we need to ensure that the slope between any two pairs of points is the same.
1. Calculate the slope between (5, 2) and (9, 5):
Slope_1 = (5 – 2) / (9 – 5) = 3 / 4
2. Calculate the slope between (1, x) and (5, 2):
Slope_2 = (2 – x) / (5 – 1) = (2 – x) / 4
3. Set the slopes equal to each other:
(2 – x) / 4 = 3 / 4
4. Solve for x:
2 – x = 3
-x = 3 – 2
-x = 1
x = -1
Answer: (D) -1
