Coordinate Geometry and Geometric Shapes Quiz

Test your knowledge of coordinate geometry with questions on midpoint formula, circle equations, line equations, shapes, and more.

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

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

((x1 - x2) / 2, (y1 - y2) / 2)

((x2 - x1) / 2, (y2 - y1) / 2)

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

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

x^2 + y^2 = r^2

y = mx + c

y = a(x - h)^2 + k

y = |x|

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

(1, 1)

(1, -1)

(2, -1)

(4, 2)

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

y = x^2 + 2x - 3

y = (x - 2)^2 - 3

y = (x + 2)^2 - 3

y = x^2 - 2x - 3

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

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

x = c

y = mx + c

y = c

x = mx + c

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

2x - 3y = 10

3x - 2y = 8

2x + 3y = 10

3x + 2y = 8

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

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

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

y = -x + 2

y = x + 2

y = -x - 2

y = x - 2

#10

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

(x - 3)^2 + (y + 2)^2 = 4

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

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

(x + 3)^2 + (y - 2)^2 = 4

#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?

#12

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

x = a constant

y = a constant

y = mx + c

x = 0

#13

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

9 square units

11 square units

12 square units

14 square units

#14

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

√20

#15

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

(3, 4)

(2, 3)

(4, 6)

(2, 4)

Coordinate Geometry and Geometric Shapes Quiz

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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