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Coordinate Geometry Calculations Quiz

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#1

Which of the following represents the midpoint formula in a coordinate plane?

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

Average of x-coordinates and y-coordinates of two points.

#2

What is the equation of a vertical line passing through the point (4, -3)?

x = 4
Explanation

x-coordinate remains constant for all points on a vertical line.

#3

Which of the following represents the slope-intercept form of a linear equation?

y = mx + b
Explanation

y-intercept form of a linear equation.

#4

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

y = 1/2x - 2
Explanation

Negative reciprocal slopes for perpendicular lines.

#5

What are the coordinates of the image of point (3, -2) after a reflection over the x-axis?

(3, -2)
Explanation

Reflection over the x-axis keeps the x-coordinate the same and negates the y-coordinate.

#6

What is the slope of a line parallel to the line represented by the equation y = 3x - 2?

3
Explanation

Parallel lines have equal slopes.

#7

What is the distance between the points (1, 2) and (-2, 5) in a coordinate plane?

√13
Explanation

Calculated using the distance formula.

#8

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

8 square units
Explanation

Using the formula for the area of a triangle.

#9

What is the equation of a circle with its center at (-3, 4) and a radius of 5 units?

(x + 3)^2 + (y - 4)^2 = 5^2
Explanation

Standard form equation of a circle.

#10

What is the distance between the point (2, -1) and the line represented by the equation 3x + 4y = 12?

3
Explanation

Distance between a point and a line formula.

#11

What are the coordinates of the intersection point of the lines represented by the equations 2x + y = 7 and x - 3y = 1?

(3, 1)
Explanation

Solving the system of linear equations.

#12

What is the equation of the line passing through the points (1, 2) and (5, -3) in a coordinate plane?

y = -11/6x + 5/6
Explanation

Using the two-point form of a linear equation.

#13

What is the distance between the points (-1, 2) and (5, -3) in a coordinate plane?

7
Explanation

Calculated using the distance formula.

#14

What are the coordinates of the centroid of the triangle with vertices at (1, 2), (4, 5), and (7, 1)?

(4, 3)
Explanation

Centroid coordinates are the averages of corresponding coordinates of triangle vertices.

#15

What are the coordinates of the intersection point of the lines represented by the equations 3x + 4y = 12 and 6x - 2y = 4?

(2, 1)
Explanation

Solving the system of linear equations.

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