Geometry: Properties of Perpendicular Lines

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Questions and Answers

Which of the following statements about lines m and k is true given they are perpendicular?

The slopes of lines m and k are equal in magnitude.
Line m and line k do not intersect.
Line m and line k have the same slope.
The product of the slopes of lines m and k is -1. (correct)

When lines m and k intersect, what is the sum of their slopes?

2
-1
0 (correct)
1

If line m is perpendicular to line k, which of the following statements could be true?

Line m and line k intersect. (correct)
Line m and line k run parallel to each other.
The slopes of lines m and k are both positive.
Line m creates an obtuse angle at the intersection with line k.

Which of these characteristics does NOT apply to perpendicular lines m and k?

They have slopes that are positive. (D) Signup and view all the answers

What can be inferred about the angle created by line m at the intersection with line k?

It must be a right angle. (B) Signup and view all the answers

Which statement is true regarding two lines in the same plane that do not intersect?

The lines must be parallel. (D) Signup and view all the answers

Is it true that if two lines in space do not intersect, they must be parallel?

No, they might be skew lines. (C) Signup and view all the answers

Which statement is correct regarding parallel lines?

If lines are parallel, they must lie in the same plane. (D) Signup and view all the answers

What can be concluded about two lines that are parallel?

They may be skew to another line. (B) Signup and view all the answers

Which of the following statements is incorrect?

Lines in space that do not intersect are parallel. (B) Signup and view all the answers

Which statement is true regarding points J, K, and L?

J, K, and L are coplanar. (A) Signup and view all the answers

What can be said about the segments JK and KL?

JK is equal to KL. (C) Signup and view all the answers

Which of the following cannot be concluded based on JK = KL?

K is the midpoint of JL. (A), The measure of ∠JKL is 90°. (C) Signup and view all the answers

If J, K, and L are coplanar, which of the following must also be true?

Intervals JK and KL are equal. (A), The measure of ∠JKL could be any angle. (C) Signup and view all the answers

Which statement is NOT a necessary conclusion based on JK = KL?

K is the midpoint of JL. (B) Signup and view all the answers

Which statement about lines in the same plane is true?

If two lines do not intersect, they must be parallel. (D) Signup and view all the answers

Which statement regarding lines in space is correct?

If two lines do not intersect, they may be skew lines. (D) Signup and view all the answers

What can be concluded if two lines are parallel?

They must lie in the same plane. (A) Signup and view all the answers

Which of the following options is incorrect regarding non-intersecting lines?

Non-intersecting lines in the same plane must be skew. (D) Signup and view all the answers

What is false about lines that are parallel?

They can be in different planes. (B) Signup and view all the answers

What is the slope of the longer base of the trapezoid?

$rac{2}{3}$ (B) Signup and view all the answers

Which point is used to find the equation of the line containing the shorter base?

(3, 1) (B) Signup and view all the answers

Using the point-slope form, which equation represents the line containing the shorter base before simplification?

$y - 1 = \frac{2}{3}(x - 3)$ (B) Signup and view all the answers

What is the final equation of the line containing the shorter base after simplification?

$y = \frac{2}{3}x - 1$ (C) Signup and view all the answers

If the slope of both bases of a trapezoid is equal, what can be inferred about their lines?

They are parallel to each other. (A) Signup and view all the answers

What is the slope of the longer base of the trapezoid?

2/3 (D) Signup and view all the answers

Which equation correctly represents the shorter base of the trapezoid?

y = rac{2}{3}x - 1 (D) Signup and view all the answers

Given the point (3, 1) on the shorter base, which form of the equation was used to derive its line equation?

Point-slope form (C) Signup and view all the answers

What characteristic do the bases of a trapezoid share?

They are parallel to each other. (C) Signup and view all the answers

What is the vertical intercept of the shorter base's line equation $y = rac{2}{3}x - 1$?

-1 (C) Signup and view all the answers

What is the result of reflecting rectangle PQRS across the x-axis?

Rectangle P'Q'R'S' is formed. (A) Signup and view all the answers

What is necessary to transform rectangle P'Q'R'S' back to PQRS after reflecting across the x-axis?

A reflection across the y-axis followed by a 180° rotation around the origin. (A) Signup and view all the answers

Which transformation would NOT return rectangle P'Q'R'S' to rectangle PQRS?

Two consecutive reflections across the x-axis. (A) Signup and view all the answers

After rectangle PQRS is reflected across the x-axis, which point changes its coordinates from (x, y) to (x, -y)?

(x1, y1) (C) Signup and view all the answers

Which transformation sequence describes a method to transform rectangle PQRS back from its reflection P'Q'R'S'?

Reflection across the y-axis followed by a 180° rotation around the origin. (D) Signup and view all the answers

Flashcards

Coplanar Points

Points that lie on the same plane.

Collinear Points

Points that lie on the same line.