Question

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)

Answer 1

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* m_2=-1`

`2* m_2=-1`

`m_2=-(1)/(2)`

So, slope of perpendicular line is
`-(1)/(2)`.

Point slope form of the perpendicular line is

`y-(7)=-(1)/(2)(x-(-3))`

`y-7=-(1)/(2)(x+3)`

Therefore, the correct option is C.