Geometric Properties in the Coordinate Plane Quiz

Test your knowledge of midpoint, distance formula, slope-intercept form, and more in the coordinate plane. Practice now!

Practice Learn Test

What is the midpoint formula in the coordinate plane?

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

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

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

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

What are the coordinates of the origin in the Cartesian coordinate system?

(0, 1)

(1, 0)

(0, 0)

(1, 1)

What is the y-intercept of the line with equation y = 3x - 2 in the coordinate plane?

-3

-2

What is the slope of a horizontal line in the coordinate plane?

Undefined

-1

What are the coordinates of the y-intercept of the line with equation y = -2x + 5 in the coordinate plane?

(0, -2)

(0, 5)

(5, 0)

(-2, 0)

What is the distance formula between two points in the coordinate plane?

√(x2 - x1)^2 + (y2 - y1)^2

(x2 - x1)^2 + (y2 - y1)^2

(x2 + x1)^2 + (y2 + y1)^2

√(x2 + x1)^2 + (y2 + y1)^2

What is the slope-intercept form of a linear equation?

y = mx + b

y = mx - b

y = bx + m

y = bx - m

What are the coordinates of the vertex of a parabola in vertex form?

(h, k)

(k, h)

(0, 0)

(0, k)

What does the discriminant of a quadratic equation determine?

Number of x-intercepts

Number of y-intercepts

Nature of roots

Coefficient of x

#10

What is the equation of a perpendicular bisector of a line segment in the coordinate plane?

y = mx + c

y = -mx + c

y = mx - c

y = -mx - c

#11

Which of the following transformations preserves the lengths of segments in the coordinate plane?

Translation

Rotation

Reflection

Dilation

#12

What is the equation of a vertical line passing through the point (-3, 2)?

x = -3

y = -3

x = 2

y = 2

#13

Which of the following transformations changes the size of a figure in the coordinate plane without changing its shape?

Rotation

Reflection

Translation

Dilation

#14

What is the equation of a line perpendicular to y = 2x + 3 passing through the point (2, -1) in the coordinate plane?

y = 2x + 5

y = -2x + 5

y = -2x - 1

y = 2x - 1

#15

What is the midpoint of the line segment with endpoints (1, 2) and (5, 8) in the coordinate plane?

(3, 5)

(2, 6)

(4, 7)

(6, 9)

#16

What is the equation of a horizontal line in the coordinate plane?

y = mx + b

y = constant

x = constant

x = my + b

#17

Which of the following is a property of a rhombus in the coordinate plane?

All sides are equal

Opposite sides are parallel

All angles are right angles

Diagonals bisect each other

#18

In the coordinate plane, what is the equation of a circle with center (h, k) and radius r?

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

(x + h)^2 + (y + k)^2 = r

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

(x + h)^2 + (y + k)^2 = r^2

#19

What is the area of a triangle formed by three points A(x1, y1), B(x2, y2), and C(x3, y3) in the coordinate plane?

|(x1y2 + x2y3 + x3y1 - x1y3 - x2y1 - x3y2)|

|(x1y2 - x2y1) + (x2y3 - x3y2) + (x3y1 - x1y3)|

|(x1y2 - x2y1) - (x2y3 - x3y2) - (x3y1 - x1y3)|

|(x1y2 + x2y1) - (x2y3 + x3y2) + (x3y1 - x1y3)|

#20

What is the equation of a vertical line passing through the point (5, 3)?

x = 5

y = 5

x = 3

y = 3

#21

What is the equation of the line passing through points (2, 3) and (4, 7) in the coordinate plane?

y = 2x + 1

y = 2x - 1

y = 2x + 5

y = 2x - 5

#22

What are the coordinates of the circumcenter of a triangle in the coordinate plane?

Midpoint of any side

Intersection of altitudes

Intersection of perpendicular bisectors

Intersection of medians

#23

What is the equation of a circle centered at (3, -2) with radius 4 in the coordinate plane?

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

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

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

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

#24

What are the coordinates of the centroid of a triangle in the coordinate plane?