A line passes through $(9 ,2 )$ and $( 4, 5 )$ . A second line passes through $( 4, 1 )$ . 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 · 2017-02-13T08:36:15

$(-6,7)$

Two parallel lines have the same gradient.

When we calculate the gradient of the first line,

gradient = $(y_2-y_1)/(x_2-x_1)$

$(5-2)/(4-9)=-3/5$

The gradient of the second line will also be $-3/5$
We already have the coordinates $(4,1)$ for the second line,

Now let's say that it passes through the point $(x_2,y_2).$
We can take $y_2= 7.$

This is to simplify later, we can take any number for $y_2$ because there are infinitely many points on the line.

So
gradient = $-3/5$ = $(7-1)/(x_2-4)$

$5(7-1) = -3(x_2-4)$

$30=-3x_2+12$

$30-12=-3x_2$

$x_2=18/-3$

$x_2 =-6$

So the coordinates of a second point are $(-6,7)$

A line passes through (9 ,2 )(9 ,2 ) and ( 4, 5 )( 4, 5 ). A second line passes through ( 4, 1 )( 4, 1 ). What is one other point that the second line may pass through if it is parallel to the first line?