Mathematics: Which of these is a point-slope equation of the line that is perpendicular to y- 25 =2(x- 10) and passes through (-3, 7)? A. y-7= -2(x+ 3) B. y+7=--3) C.y-7- -x+3) D. y+7 = 2(x- 3)

The answer is B.Step-by-step explanation:...

Which of these is a point-slope equation of the line

Jonny13Diaz

14.02.2022

Given:

Equation of line is y-25=2(x-10) .

A line is perpendicular to the given line and passes through (-3,7).

To find:

The point slope form of the perpendicular line.

Solution:

Point slope form of a line is

y-y_1=m(x-x_1) ...(i)

where, (x_1,y_1) is the point from which the line is passing through and m is slope.

We have,

y-25=2(x-10) ...(ii)

From (i) and (ii), we get

m_1=2

Product of slopes of two perpendicular lines is -1.

$m_1\times m_2=-1$

$2\times m_2=-1$

$m_2=-\dfrac{1}{2}$

So, slope of perpendicular line is $-\dfrac{1}{2}$ .

Point slope form of the perpendicular line is

$y-(7)=-\dfrac{1}{2}(x-(-3))$

$y-7=-\dfrac{1}{2}(x+3)$

Therefore, the correct option is C.

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