Coordinate Geometry

Q. What is the area of a trapezoid with bases of lengths 5 and 7 and a height of 4?

Solution

Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24.

Correct Answer: A — 24

Q. What is the distance from the point (1, 2) to the line 3x + 4y - 10 = 0?

Solution

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1/5 = 0.2.

Correct Answer: A — 1

Q. What is the equation of a circle with center at (2, -3) and radius 4?

Solution

Equation of circle: (x-h)² + (y-k)² = r² => (x-2)² + (y+3)² = 4² = 16.

Correct Answer: A — (x-2)² + (y+3)² = 16

Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 4), (3, 0), and (3, 4)?

Solution

Diagonal = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5.

Correct Answer: A — 5

Q. What is the slope of the line perpendicular to the line with slope 3?

Solution

The slope of the perpendicular line is the negative reciprocal: -1/3.

Correct Answer: A — -1/3

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