MCQ
Geometry, coordinate geometry and basic trigonometry MCQ - Practice Questions with Answers
Solve 10 Geometry, coordinate geometry and basic trigonometry questions for RAS/RPSC preparation.
Practice questions
Q1Statement 1: The midpoint of the points (2, 4) and (8, 10) is (5, 7). Statement 2: The midpoint is found by taking the average of the x-coordinates and the average of the y-coordinates. Which of the following is correct?
The midpoint is given as the average of the two x-coordinates and the average of the two y-coordinates. For (2, 4) and (8, 10), the x-coordinate of the midpoint is (2 + 8) / 2 = 5, and the y-coordinate is (4 + 10) / 2 = 7. Therefore the midpoint is (5, 7). The rule stated in the second statement is also the same rule used in this calculation.
Q2Statement 1: In a triangle, the sum of the three interior angles is 180°. Statement 2: An exterior angle of a triangle equals the sum of the two opposite interior angles. Which option is correct?
There are two core triangle rules. First, the sum of the interior angles of any triangle is 180°. Second, an exterior angle equals the sum of the two opposite interior angles. These are separate but compatible facts: the exterior angle is formed by extending a side, while the 180° rule applies inside the triangle. Since both statements repeat the rules exactly, both statements are correct.
Q3Two parallel lines are cut by a transversal. One interior angle on the same side of the transversal is 115°. What is the other interior angle on the same side?
When a transversal cuts two parallel lines, interior angles on the same side of the transversal add to 180°. The given angle is 115°, so the other same-side interior angle must be 180° - 115° = 65°. Equal-angle rules apply to corresponding angles and alternate interior angles, not to this same-side interior pair.
Q4Assertion (A): If a tower is 20 m away from a point and the angle of elevation from that point is 45°, the height of the tower is 20 m. Reason (R): In a right triangle, tan 45° = 1, and tan angle = height / distance in such height-distance questions. Choose the correct answer.
In height-distance questions the height, ground distance and line of sight form a right triangle. When height is asked and distance is given, tan angle = height / distance is often the fastest ratio. Here tan 45° = 1, so 1 = height / 20. Hence height = 20 m. The reason is not only true; it is exactly the rule that proves the assertion.
Q5List I: 1. Horizontal line 2. Vertical line 3. Parallel non-vertical lines List II: P. Undefined slope Q. Equal slopes R. Slope 0 Choose the correct matching.
Slope is defined as change in y divided by change in x, when the change in x is not zero. A horizontal line has no change in y, so its slope is 0. A vertical line has no change in x, so division by zero would occur and its slope is undefined. Parallel non-vertical lines have equal slopes. Therefore the correct matching is horizontal line with slope 0, vertical line with undefined slope, and parallel non-vertical lines with equal slopes.
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More questions
6A rectangular floor is 12 m long and 8 m broad. Which measurement is needed to tile the whole floor?
7A rectangular school ground is 40 m long and 25 m broad. How much wire is needed to fence it once around the boundary?
8List I gives two coordinate-geometry tasks. Match them with the correct result. List I: 1. Distance between (1, 2) and (4, 6) 2. Midpoint of (2, 4) and (8, 10) List II: P. (5, 7) Q. 5 units R. (3, 4) S. 7 units
9Assertion (A): If two tangents are drawn from the same external point to a circle and one tangent is 7 cm long, the other tangent is also 7 cm long. Reason (R): Tangents drawn from the same external point to a circle are equal in length.
10A person stands 20 m from the foot of a tower. The angle of elevation to the top of the tower is 45°. What is the height of the tower?