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Geometric Properties in the Coordinate Plane Quiz

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#1

What is the midpoint formula in the coordinate plane?

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

Average of x and y coordinates

#2

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

(0, 0)
Explanation

Point of intersection of x and y axes

#3

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

-2
Explanation

Point where line crosses y-axis

#4

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

0
Explanation

No change in y

#5

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

(0, 5)
Explanation

Point where line crosses y-axis

#6

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

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

Pythagorean theorem

#7

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

y = mx + b
Explanation

y-intercept and slope

#8

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

(h, k)
Explanation

Coordinates of the vertex

#9

What does the discriminant of a quadratic equation determine?

Nature of roots
Explanation

Type of roots (real, imaginary)

#10

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

y = -mx + c
Explanation

Negative reciprocal slope

#11

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

Translation
Explanation

Shifting without resizing

#12

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

x = 2
Explanation

Constant x value

#13

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

x = constant
Explanation

Constant x value

#14

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

Diagonals bisect each other
Explanation

Halving diagonals

#15

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
Explanation

Standard circle equation

#16

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)|
Explanation

Shoelace formula

#17

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

x = 5
Explanation

Constant x value

#18

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

y = 2x - 1
Explanation

Slope-intercept form

#19

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

Intersection of perpendicular bisectors
Explanation

Common point of bisectors

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