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 · 2016-04-07T08:52:23

The other point is $(5, 6)$ $(5, 6)$

Slope is equal to slope

Let $A (8, 5)$ $A(8, 5)$ and $B (6, 4)$ $B(6, 4)$ and $C (3, 5)$ $C(3, 5)$
Let $D (x, y)$ $D(x, y)$ the unknown point

slope A to B = slope D to C

$\frac{5 - 4}{8 - 6} = \frac{y - 5}{x - 3}$ $(5-4)/(8-6)=(y-5)/(x-3)$
$x - 2 y = - 7$ $x-2y=-7" "$ first equation

slope B to C = slope A to D
$\frac{y - 5}{x - 8} = \frac{5 - 4}{3 - 6}$ $(y-5)/(x-8)=(5-4)/(3-6)$
$x + 3 y = 23$ $x+3y=23" "$ second equation

Simultaneous solution of first and second equations results to
$D (x, y) = (5, 6)$ $D(x, y)=(5, 6)$

God bless....I hope the explanation is useful.

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?