Math / Geometry

QuestionUse slopes to determine if the lines are parallel, perpendicular, or neither.
28. $\overleftrightarrow{J K}$ and $\overleftrightarrow{L M}$ for $J(4,3), K(-4,-2), L(5,6)$ , and

Studdy Solution

STEP 1

1. Two lines are parallel if their slopes are equal.
2. Two lines are perpendicular if the product of their slopes is $-1$ .
3. The slope of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 2

1. Calculate the slope of line $\overleftrightarrow{JK}$ .
2. Calculate the slope of line $\overleftrightarrow{LM}$ .
3. Compare the slopes to determine if the lines are parallel, perpendicular, or neither.

STEP 3

Calculate the slope of line $\overleftrightarrow{JK}$ using points $J(4, 3)$ and $K(-4, -2)$ .
$m_{JK} = \frac{-2 - 3}{-4 - 4}$

STEP 4

Simplify the expression for $m_{JK}$ .
$m_{JK} = \frac{-5}{-8} = \frac{5}{8}$

STEP 5

Calculate the slope of line $\overleftrightarrow{LM}$ using points $L(5, 6)$ and $M(-3, 1)$ .
$m_{LM} = \frac{1 - 6}{-3 - 5}$

STEP 6

Simplify the expression for $m_{LM}$ .
$m_{LM} = \frac{-5}{-8} = \frac{5}{8}$

STEP 7

Compare the slopes $m_{JK}$ and $m_{LM}$ .
Since $m_{JK} = m_{LM} = \frac{5}{8}$ , the lines $\overleftrightarrow{JK}$ and $\overleftrightarrow{LM}$ are parallel.
The lines $\overleftrightarrow{JK}$ and $\overleftrightarrow{LM}$ are parallel.

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QuestionUse slopes to determine if the lines are parallel, perpendicular, or neither.
28. $\overleftrightarrow{J K}$ and $\overleftrightarrow{L M}$ for $J(4,3), K(-4,-2), L(5,6)$ , and

Studdy Solution

STEP 1

1. Two lines are parallel if their slopes are equal.
2. Two lines are perpendicular if the product of their slopes is $-1$ .
3. The slope of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

STEP 2

1. Calculate the slope of line $\overleftrightarrow{JK}$ .
2. Calculate the slope of line $\overleftrightarrow{LM}$ .
3. Compare the slopes to determine if the lines are parallel, perpendicular, or neither.

STEP 3

Calculate the slope of line $\overleftrightarrow{JK}$ using points $J(4, 3)$ and $K(-4, -2)$ .
$m_{JK} = \frac{-2 - 3}{-4 - 4}$

STEP 4

Simplify the expression for $m_{JK}$ .
$m_{JK} = \frac{-5}{-8} = \frac{5}{8}$

STEP 5

Calculate the slope of line $\overleftrightarrow{LM}$ using points $L(5, 6)$ and $M(-3, 1)$ .
$m_{LM} = \frac{1 - 6}{-3 - 5}$

STEP 6

Simplify the expression for $m_{LM}$ .
$m_{LM} = \frac{-5}{-8} = \frac{5}{8}$

STEP 7

Compare the slopes $m_{JK}$ and $m_{LM}$ .
Since $m_{JK} = m_{LM} = \frac{5}{8}$ , the lines $\overleftrightarrow{JK}$ and $\overleftrightarrow{LM}$ are parallel.
The lines $\overleftrightarrow{JK}$ and $\overleftrightarrow{LM}$ are parallel.

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QuestionUse slopes to determine if the lines are parallel, perpendicular, or neither.28. JKundefined\overleftrightarrow{J K}JK and LMundefined\overleftrightarrow{L M}LM for J(4,3),K(−4,−2),L(5,6)J(4,3), K(-4,-2), L(5,6)J(4,3),K(−4,−2),L(5,6), and

Studdy Solution

STEP 1

STEP 2

1. Calculate the slope of line JKundefined\overleftrightarrow{JK}JK.2. Calculate the slope of line LMundefined\overleftrightarrow{LM}LM.3. Compare the slopes to determine if the lines are parallel, perpendicular, or neither.

STEP 3

Calculate the slope of line JKundefined\overleftrightarrow{JK}JK using points J(4,3)J(4, 3)J(4,3) and K(−4,−2)K(-4, -2)K(−4,−2).mJK=−2−3−4−4 m_{JK} = \frac{-2 - 3}{-4 - 4} mJK​=−4−4−2−3​

STEP 4

Simplify the expression for mJKm_{JK}mJK​.mJK=−5−8=58 m_{JK} = \frac{-5}{-8} = \frac{5}{8} mJK​=−8−5​=85​

STEP 5

Calculate the slope of line LMundefined\overleftrightarrow{LM}LM using points L(5,6)L(5, 6)L(5,6) and M(−3,1)M(-3, 1)M(−3,1).mLM=1−6−3−5 m_{LM} = \frac{1 - 6}{-3 - 5} mLM​=−3−51−6​

STEP 6

Simplify the expression for mLMm_{LM}mLM​.mLM=−5−8=58 m_{LM} = \frac{-5}{-8} = \frac{5}{8} mLM​=−8−5​=85​

STEP 7

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QuestionUse slopes to determine if the lines are parallel, perpendicular, or neither.
28. $\overleftrightarrow{J K}$ and $\overleftrightarrow{L M}$ for $J(4,3), K(-4,-2), L(5,6)$ , and

1. Calculate the slope of line $\overleftrightarrow{JK}$ .
2. Calculate the slope of line $\overleftrightarrow{LM}$ .
3. Compare the slopes to determine if the lines are parallel, perpendicular, or neither.

Calculate the slope of line $\overleftrightarrow{JK}$ using points $J(4, 3)$ and $K(-4, -2)$ .
$m_{JK} = \frac{-2 - 3}{-4 - 4}$

Simplify the expression for $m_{JK}$ .
$m_{JK} = \frac{-5}{-8} = \frac{5}{8}$

Calculate the slope of line $\overleftrightarrow{LM}$ using points $L(5, 6)$ and $M(-3, 1)$ .
$m_{LM} = \frac{1 - 6}{-3 - 5}$

Simplify the expression for $m_{LM}$ .
$m_{LM} = \frac{-5}{-8} = \frac{5}{8}$