A line passes through $(8, 5)$ $(8 ,5 )$ and $(6, 4)$ $(6 ,4 )$ . A second line passes through $(3, 5)$ $(3 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(8, 5)$ $(8 ,5 )$ and $(6, 4)$ $(6 ,4 )$ . A second line passes through $(3, 5)$ $(3 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-09-22T06:58:47

Any point other than $(7, 6)$ $(7,6)$ and satisfying the condition $x - 2 y + 7 = 0$ $x-2y+7=0$ could be such a point. Examples are $(- 5, 1)$ $(-5,1)$ , $(7, 7)$ $(7,7)$ and $(- 1, 3)$ $(-1,3)$ .

Explanation:

A line passing through $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ has a slope of $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$ . Hence slope of line joining $(8, 5)$ $(8,5)$ and $(6, 4)$ $(6,4)$ is

$\frac{4 - 5}{6 - 8} = \frac{- 1}{- 2} = \frac{1}{2}$ $(4-5)/(6-8)=(-1)/(-2)=1/2$

As the second line passing through $(3, 5)$ $(3,5)$ is parallel to the above, its slope too is $\frac{1}{2}$ $1/2$ .

Now, equation of a line passing through $(x_{1}, y_{1})$ $(x_1,y_1)$ and having a slope of $m$ $m$ is $(y - y_{1}) = m (x - x_{1})$ $(y-y_1)=m(x-x_1)$ . Hence, the equation of line passing through $(3, 5)$ $(3,5)$ and having a slope of $\frac{1}{2}$ $1/2$ is

$(y - 5) = \frac{1}{2} (x - 3)$ $(y-5)=1/2(x-3)$ or $2 y - 10 = x - 3$ $2y-10=x-3$ i.e. $x - 2 y + 7 = 0$ $x-2y+7=0$

Hence, any point satisfying the condition $x - 2 y + 7 = 0$ $x-2y+7=0$ (other than $(3, 5)$ $(3,5)$ will satisfy this.

Let $x = - 5$ $x=-5$ then $y = 1$ $y=1$ , hence point could be $(- 5, 1)$ $(-5,1)$ or

let $x = 7$ $x=7$ then $y = 7$ $y=7$ , hence other point could be $(7, 7)$ $(7,7)$ or

let $x = - 1$ $x=-1$ then $y = 3$ $y=3$ , hence point could be $(- 1, 3)$ $(-1,3)$

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A line passes through $(8, 5)$ $(8 ,5 )$ and $(6, 4)$ $(6 ,4 )$ . A second line passes through $(3, 5)$ $(3 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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A line passes through (8 ,5 )(8,5)(8 ,5 ) and (6 ,4 )(6,4)(6 ,4 ). A second line passes through (3 ,5 )(3,5)(3 ,5 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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A line passes through $(8, 5)$ $(8 ,5 )$ and $(6, 4)$ $(6 ,4 )$ . A second line passes through $(3, 5)$ $(3 ,5 )$ . What is one other point that the second line may pass through if it is parallel to the first line?