Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

There are two parallel lines with one passing through $(d, 3)$ & $(-2,1)$ and the second line passes through $(5,d)$ & $(1,0)$.

Find the two values for $d$.

I found one value would be $-4$. But how would I do this to find the second value?

share|improve this question

1 Answer 1

up vote 0 down vote accepted

If two lines are parallel, then the slope of both the lines are equal.

If a line passes through the points, $(x_1,y_1)$ and $(x_2,y_2)$, then the slop of the line is given by $$\text{Slope } = \dfrac{y_1 - y_2}{x_1 - x_2}$$

The first line passes through the points $(d,3)$ and $(-2,1)$. Hence, the slope of the first line is $$\dfrac{3-1}{d-(-2)}$$

The second line passes through the points $(5,d)$ and $(1,0)$. Hence, the slope of the second line is $$\dfrac{d-0}{5-1}$$

Since the lines are parallel, the slope are equal. Equate the two to get $$\dfrac2{d+2} = \dfrac{d}4 \implies d^2+2d = 8 \implies d^2 +2d-8 = 0$$ Can you now finish it off?

Move your mouse over the gray area for the final answer.

$$d^2 + 2d - 8 = 0 \implies (d+4)(d-2) = 0 \implies d= 2 \text{ or } -4$$

share|improve this answer
    
If I am correct, the solution would be 2. Correct? –  user34548 Jul 1 '12 at 0:17
    
@Michael Yes. $2$ and $-4$ are the desired slopes. –  user17762 Jul 1 '12 at 0:18
    
Thanks so much. –  user34548 Jul 1 '12 at 0:21

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.