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Coordinate Geometry and Geometric Shapes Quiz

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#1

What is the midpoint formula for a line segment with endpoints (x1, y1) and (x2, y2)?

((x1 + x2) / 2, (y1 + y2) / 2)
Explanation

Average x and y coordinates of endpoints.

#2

Which of the following equations represents a circle in the Cartesian plane?

x^2 + y^2 = r^2
Explanation

Standard form of a circle equation.

#3

What are the coordinates of the midpoint of the line segment joining the points (-3, 4) and (5, -2)?

(2, -1)
Explanation

Average x and y coordinates of endpoints.

#4

Which of the following is the equation of a parabola with its vertex at (2, -3)?

y = (x - 2)^2 - 3
Explanation

Vertex form of a parabola equation.

#5

What is the distance between the points (2, -3) and (-4, 5) in the Cartesian plane?

8
Explanation

Distance formula between two points.

#6

The equation of a line parallel to the y-axis is of the form:

x = c
Explanation

Vertical line with constant x.

#7

What is the equation of the line perpendicular to the line passing through points (3, 4) and (5, 2)?

3x - 2y = 8
Explanation

Negative reciprocal slope.

#8

In a coordinate plane, which quadrant is characterized by positive x-values and negative y-values?

Quadrant III
Explanation

Bottom-left quadrant.

#9

What is the equation of the line passing through the points (-1, 3) and (4, -2)?

y = -x + 2
Explanation

Slope-intercept form using given points.

#10

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

(x - 3)^2 + (y + 2)^2 = 16
Explanation

Standard form of a circle equation.

#11

The coordinates of the vertices of a rectangle are A(2, 3), B(6, 3), C(6, -1), and D(2, -1). What is the length of the diagonal BD?

5
Explanation

Distance between points using Pythagorean theorem.

#12

If the slope of a line is undefined, what is the equation of that line?

x = a constant
Explanation

Vertical line with constant x.

#13

What is the area of the triangle formed by the points (1, 2), (4, 5), and (-3, 4)?

11 square units
Explanation

Use coordinates to find triangle's area.

#14

If a circle has its center at (1, 3) and passes through the point (5, 7), what is its radius?

4
Explanation

Distance between center and any point on circle.

#15

What are the coordinates of the circumcenter of a triangle with vertices at (0, 0), (6, 0), and (0, 8)?

(3, 4)
Explanation

Intersection of perpendicular bisectors.

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