Coordinate Geometry

Q. What is the area of a circle with a radius of 7?

Solution

Area = πr² = π(7)² = 49π.

Correct Answer: A — 49π

Q. What is the distance between the points (3, 4) and (7, 1)?

Solution

Using the distance formula: d = √((x2 - x1)² + (y2 - y1)²) = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.

Correct Answer: A — 5

Q. What is the equation of a circle with center (2, -3) and radius 5?

Solution

Standard form of a circle: (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. Thus, (x - 2)² + (y + 3)² = 5² = 25.

Correct Answer: A — (x - 2)² + (y + 3)² = 25

Q. What is the equation of the line with a slope of 2 that passes through the point (1, 1)?

Solution

Using point-slope form: y - y1 = m(x - x1) => y - 1 = 2(x - 1) => y = 2x - 2 + 1 => y = 2x - 1.

Correct Answer: A — y = 2x + 1

Q. What is the length of the diagonal of a rectangle with length 6 and width 8?

Solution

Using the Pythagorean theorem: d = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10.

Correct Answer: A — 10

Q. What is the length of the line segment between the points (-1, -1) and (3, 3)?

Solution

Using the distance formula: d = √((3 - (-1))² + (3 - (-1))²) = √((4)² + (4)²) = √(16 + 16) = √32 = 4√2.

Correct Answer: A — 4√2

Q. What is the midpoint of the line segment joining the points (2, 3) and (4, 7)?

Solution

Midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 7)/2) = (3, 5).

Correct Answer: A — (3, 5)

Q. What is the slope of the line passing through the points (1, 2) and (3, 6)?

Solution

Slope formula: m = (y2 - y1) / (x2 - x1) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Correct Answer: A — 2

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

Solution

The slope of a line perpendicular to another is the negative reciprocal. Thus, the slope is 1/3.

Correct Answer: A — 1/3

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