A line passes through $(4, 3)$ $(4 ,3 )$ and $(2, 6)$ $(2 ,6 )$ . A second line passes through $(1, 8)$ $(1 ,8 )$ . 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 · 2018-06-19T14:03:26

$(2, \frac{13}{2})$ $color(blue)((2,13/2)$

If two lines are parallel then their gradients are the same.

Gradient of line passing through points $(4, 3), (2, 6)$ $(4,3),(2,6)$

Let $m$ $m$ be the gradient:

Then:

$m = \frac{6 - 3}{2 - 4} = - \frac{3}{2}$ $m=(6-3)/(2-4)=-3/2$

The line passing through point $(1, 8)$ $(1,8)$ also has gradient $- \frac{3}{2}$ $-3/2$

Equation of this line using point slope form:

$(y_{2} - y_{1}) = m (x_{2} - x_{1})$ $(y_2-y_1)=m(x_2-x_1)$

$y - 8 = - \frac{3}{2} (x - 1)$ $y-8=-3/2(x-1)$

$y = - \frac{3}{2} x + \frac{19}{2}$ $y=-3/2x+19/2$

So another point on the line passing through point $(1, 8)$ $(1,8)$ and parallel to the other line is any point that satisfies the equation:

$y = - \frac{3}{2} x + \frac{19}{2}$ $y=-3/2x+19/2$

We could express this as.

$(x, - \frac{3}{2} x + \frac{19}{2})$ $(x,-3/2x+19/2)$

For a specific value, we could choose $x = 2$ $x=2$

$y = - \frac{3}{2} (2) + \frac{19}{2} = \frac{13}{2}$ $y=-3/2(2)+19/2=13/2$

co-ordinates:

$(2, \frac{13}{2})$ $(2,13/2)$

PLOT: enter image source here

A line passes through (4,3)(4 ,3 ) and (2,6)(2 ,6 ). A second line passes through (1,8)(1 ,8 ). What is one other point that the second line may pass through if it is parallel to the first line?