A line passes through $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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 $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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 · 2018-01-07T15:07:11

One other point is $(1, (\frac{16}{3}))$ $(1, (16/3))$ through which the second line CD will pass through

Explanation:

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Let the coordinates of A (6,4) & B (9,2)

Slope of AB $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2 - 4}{9 - 6} = - (\frac{2}{3})$ $m = (y_2 - y_1) / (x_2 - x_1) = (2 - 4) / (9 - 6) = -(2/3)$

Slope of AB = Slope of CD as they are parallel.

Equation of CD is

$(y - y_{3}) = m (x - x_{3})$ $(y - y_3) = m (x - x_3)$ where coordinates of C is (3,4)

$y - 4 = - (\frac{2}{3}) (x - 3)$ $y - 4 = -(2/3) (x - 3)$

$3 y - 12 = - 2 x + 6$ $3y - 12 = -2x + 6$

$2 x + 3 y = 18$ $2x + 3y = 18$

By Substituting different values for x, one can arrive at the corresponding value for y in the above equation.

When x = 1, $y = \frac{18 - 2}{3} = \frac{16}{3}$ $y = (18 - 2) / 3 = 16/3$

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A line passes through $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . 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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Impact of this question

Science

Math

Humanities

... and beyond

A line passes through (6,4)(6 ,4 ) and (9,2)(9 ,2 ). A second line passes through (3,4)(3 ,4 ). 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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Impact of this question

A line passes through $(6, 4)$ $(6 ,4 )$ and $(9, 2)$ $(9 ,2 )$ . A second line passes through $(3, 4)$ $(3 ,4 )$ . What is one other point that the second line may pass through if it is parallel to the first line?