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Midpoint and Segment Relationships in Geometry Quiz

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#1

Which of the following represents the midpoint formula for a line segment with endpoints (x₁, y₁) and (x₂, y₂)?

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

Average of x-coordinates and y-coordinates of endpoints.

#2

If the coordinates of endpoints of a line segment are A(2, 5) and B(8, 10), what is the midpoint of the segment AB?

(6, 8.5)
Explanation

Midpoint formula applied to given coordinates.

#3

What is the equation of the line segment with endpoints (1, 3) and (5, 9)?

y = x + 3
Explanation

Using the slope-intercept form of a line.

#4

If the midpoint of a line segment is (2, -3) and one endpoint is (-4, 8), what are the coordinates of the other endpoint?

(6, -6)
Explanation

Midpoint formula applied to given midpoint and endpoint.

#5

If the midpoint of a line segment is (3, 2) and one endpoint is (1, 4), what are the coordinates of the other endpoint?

(5, 4)
Explanation

Use midpoint formula to find missing endpoint.

#6

In a triangle, if the midpoints of two sides are connected, what type of line is formed?

Mid-segment
Explanation

Midpoints of two sides form a mid-segment.

#7

If the midpoint of a line segment is (3, -4) and one endpoint is (-1, 6), what are the coordinates of the other endpoint?

(4, -2)
Explanation

Use midpoint formula to find missing endpoint.

#8

In a quadrilateral, if the midpoints of all four sides are connected, what is formed?

Parallelogram
Explanation

Connecting midpoints creates a parallelogram.

#9

If the coordinates of endpoints of a line segment are A(3, -2) and B(7, 6), what is the midpoint of the segment AB?

(5, 3)
Explanation

Midpoint formula applied to given coordinates.

#10

In a triangle, if the midpoints of all three sides are connected, what is formed?

Centroid
Explanation

Connecting midpoints creates a centroid.

#11

Given two points A(3, -2) and B(7, 6), what are the coordinates of the point that partitions the line segment AB into a 2:3 ratio?

(5, 2)
Explanation

Apply ratio to segment to find partition point.

#12

Given three points A(1, 2), B(5, 6), and C(9, 10), which point divides the line segment AB in the ratio 3:2?

(4, 5)
Explanation

Apply ratio to segment to find partition point.

#13

Given two points A(2, -3) and B(-4, 5), what are the coordinates of the point that partitions the line segment AB into a 3:1 ratio?

(-1, 1)
Explanation

Apply ratio to segment to find partition point.

#14

If the equation of a line segment is y = 2x + 3 and one endpoint is (1, 5), what are the coordinates of the other endpoint?

(3, 7)
Explanation

Using the given equation and point to find the other endpoint.

#15

Given two points A(1, 4) and B(5, 8), what are the coordinates of the point that partitions the line segment AB into a 1:2 ratio?

(3, 6)
Explanation

Apply ratio to segment to find partition point.

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