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frozen [14]
2 years ago
11

Write and equati9n of a l8ne that passes through (1,-2) and is perpendicular to -4x+7y=21

Mathematics
1 answer:
yarga [219]2 years ago
7 0

Given:

A line passes through (1,-2) and is perpendicular to -4x+7y=21.

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

-4x+7y=21

Slope of this line is

m_1=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}

m_1=-\dfrac{-4}{7}

m_1=\dfrac{4}{7}

Product of slope of two perpendicular lines is -1.

m_1\times m_2=-1

\dfrac{4}{7}\times m_2=-1

m_2=-\dfrac{7}{4}

Now, slope of required line is -\dfrac{7}{4} and it passes through (1,-2). So, the equation of line is

y-y_1=m(x-x_1)

where, m is slope.

y-(-2)=-\dfrac{7}{4}(x-1)

4(y+2)=-7(x-1)

4y+8=-7x+7

4y+7x=7-8

7x+4y=-1

Therefore, the equation of required line is 7x+4y=-1.

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