Question

On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6). Which point is on the line that passes through (0, 6) and is parallel to the given line? (–12, 8) (–6, 6) (2, 8) (6, 0)

Answer 1

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GIVEN

• On a coordinate plane, a line goes through (- 12, - 2) and (0, - 4)

• A point is at (0, 6).

• A line that passes through (0, 6) and is parallel to the given line

TO CHOOSE THE CORRECT OPTION

The point which lies on the line

• (–12, 8)

• (–6, 6)

• (2, 8)

• (6, 0)

CALCULATION

The equation of the line passing through the points (- 12, - 2) and (0, - 4) is

$\displaystyle \sf{ \: \frac{y + 4}{x - 0} } = \frac{ - 4 + 2}{0 + 12}$

$\implies\displaystyle \sf{ \: \frac{y + 4}{x } } = \frac{ - 2}{ 12}$

$\implies\displaystyle \sf{x + 6y + 24 = 0 \: \: \: ....(1) }$

Now the equation of the line parallel to Equation (1) is

$\sf{ x + 6y = k \: \: \: \: ......(2)\: }$

Now Equation (2) passes through the point (0,6)

So

$\sf{0 + 36 = k}$

$\implies\sf{ k = 36}$

Equation (2) becomes

$\sf{ x + 6y = 36\: } \: \: ....(3)$

In order to find the point which lies on the line we check by putting the values of x & y in Equation (3)

Here

$\sf{ - 12 +( 8 \times 6) = - 12 + 48 = 36\: }$

So ( - 12, 8) satisfies the Equation (3)

Hence the required point is ( - 12 , 8 )

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LEARN MORE FROM BRAINLY

The point (2, -3) lies in the third quadrant.

State True or False and write correct statement.

https://brainly.in/question/4775096

Answer 2

Answer:

-12, 8

Step-by-step explanation: