QuestionIf two lines have slopes that are negative reciprocals, are they perpendicular? A. True B. False

Studdy Solution

STEP 1

Assumptions1. The slopes of two lines are negative reciprocals of each other. . The lines are in a two-dimensional Cartesian coordinate system.

STEP 2

The slope of a line is given by the formula $m = \frac{y2 - y1}{x2 - x1}$ where $(x1, y1)$ and $(x2, y2)$ are any two points on the line.

STEP 3

If two lines are perpendicular, the product of their slopes is -1. This can be written as $m1 \cdot m2 = -1$ where $m1$ and $m2$ are the slopes of the two lines.

STEP 4

If the slopes of two lines are negative reciprocals, then we can write this as $m1 = -\frac{1}{m2}$

STEP 5

Substitute $m1$ from4 into the equation from3 $-\frac{1}{m2} \cdot m2 = -1$

STEP 6

implify the equation $-1 = -1$ This equation is true, so the statement "If the slopes of two lines are negative reciprocals, the lines are perpendicular" is true.
So, the answer is A. True.

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QuestionIf two lines have slopes that are negative reciprocals, are they perpendicular? A. True B. False

Studdy Solution

STEP 1

Assumptions1. The slopes of two lines are negative reciprocals of each other. . The lines are in a two-dimensional Cartesian coordinate system.

STEP 2

The slope of a line is given by the formula $m = \frac{y2 - y1}{x2 - x1}$ where $(x1, y1)$ and $(x2, y2)$ are any two points on the line.

STEP 3

If two lines are perpendicular, the product of their slopes is -1. This can be written as $m1 \cdot m2 = -1$ where $m1$ and $m2$ are the slopes of the two lines.

STEP 4

If the slopes of two lines are negative reciprocals, then we can write this as $m1 = -\frac{1}{m2}$

STEP 5

Substitute $m1$ from4 into the equation from3 $-\frac{1}{m2} \cdot m2 = -1$

STEP 6

implify the equation $-1 = -1$ This equation is true, so the statement "If the slopes of two lines are negative reciprocals, the lines are perpendicular" is true.
So, the answer is A. True.

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QuestionIf two lines have slopes that are negative reciprocals, are they perpendicular? A. True B. False

Studdy Solution

STEP 1

Assumptions1. The slopes of two lines are negative reciprocals of each other. . The lines are in a two-dimensional Cartesian coordinate system.

STEP 2

The slope of a line is given by the formulam=y2−y1x2−x1m = \frac{y2 - y1}{x2 - x1}m=x2−x1y2−y1​where (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) are any two points on the line.

STEP 3

If two lines are perpendicular, the product of their slopes is -1. This can be written asm1⋅m2=−1m1 \cdot m2 = -1m1⋅m2=−1where m1m1m1 and m2m2m2 are the slopes of the two lines.

STEP 4

If the slopes of two lines are negative reciprocals, then we can write this asm1=−1m2m1 = -\frac{1}{m2}m1=−m21​

STEP 5

Substitute m1m1m1 from4 into the equation from3−1m2⋅m2=−1-\frac{1}{m2} \cdot m2 = -1−m21​⋅m2=−1

STEP 6

implify the equation−1=−1-1 = -1−1=−1This equation is true, so the statement "If the slopes of two lines are negative reciprocals, the lines are perpendicular" is true.So, the answer is A. True.

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The slope of a line is given by the formula $m = \frac{y2 - y1}{x2 - x1}$ where $(x1, y1)$ and $(x2, y2)$ are any two points on the line.

If two lines are perpendicular, the product of their slopes is -1. This can be written as $m1 \cdot m2 = -1$ where $m1$ and $m2$ are the slopes of the two lines.

If the slopes of two lines are negative reciprocals, then we can write this as $m1 = -\frac{1}{m2}$

Substitute $m1$ from4 into the equation from3 $-\frac{1}{m2} \cdot m2 = -1$

implify the equation $-1 = -1$ This equation is true, so the statement "If the slopes of two lines are negative reciprocals, the lines are perpendicular" is true.
So, the answer is A. True.