Given:
Equation of line is [tex]y-25=2(x-10)[/tex].
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
[tex]y-y_1=m(x-x_1)[/tex] ...(i)
where, [tex](x_1,y_1)[/tex] is the point from which the line is passing through and m is slope.
We have,
[tex]y-25=2(x-10)[/tex] ...(ii)
From (i) and (ii), we get
[tex]m_1=2[/tex]
Product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]2\times m_2=-1[/tex]
[tex]m_2=-\dfrac{1}{2}[/tex]
So, slope of perpendicular line is [tex]-\dfrac{1}{2}[/tex].
Point slope form of the perpendicular line is
[tex]y-(7)=-\dfrac{1}{2}(x-(-3))[/tex]
[tex]y-7=-\dfrac{1}{2}(x+3)[/tex]
Therefore, the correct option is C.
