Question

Determine if JK and LM are parallel ,perpendicular, or neither. J(13,-5) K(2,6) L(-1,-5) M(-4,-2)

Answer 1

Answer:

The lines are parallel

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Find the slope JK

we have

$J(13,-5),K(2,6)$

substitute the values

$m=\frac{6+5}{2-13}$

$m=\frac{11}{-11}$

$m_J_K=-1$

step 2

Find the slope LM

we have

$L(-1,-5),M(-4,-2)$

substitute the values

$m=\frac{-2+5}{-4+1}$

$m=\frac{3}{-3}$

$m_L_M=-1$

step 3

Compare the slopes

$m_J_K=-1$

$m_L_M=-1$

so

$m_J_K=m_L_M$

therefore

The lines are parallel