From the point P(-2,4), if PQ is drawn perpendicular
to the line 7x - 24 y + 10 = 0, find the equation of the
line PQ. Also determine the length of PQ.
Answers
Given :
From the point P(-2,4) a line is drawn perpendicular to
7x - 24 y + 10 = 0
To Find :
Equation of PQ & Length of PQ
Solution :
•PQ is perpendicular to
7x-24 y+10=0
•Slope of given Line =
- ( Coefficient of x)/( Coefficient of y)
•Slope of [7x - 24 y + 10 = 0] = 7/24
•Since PQ is perpendicular to
7x - 24 y + 10 = 0
=> Slope of PQ × Slope of given line = -1
Slope of PQ = -24/7
•Also, PQ passes from point P(-2,4)
Now , Equation of PQ will be :
y -Y1 = m(x-X1)
y - 4 = (-24/7)(x-(-2))
y - 4 = (-24/7)(x + 2)
7y - 28 = -24x -48
24x +7y + 20 = 0
•Now distance of a point P(a , b)
from a line Ax + By + C = 0 is given by ,
Distance = |A(a) + B(b) + C|/√(A²+B²)
•Now ,
PQ = |7(-2) + (-24)(4) + 10|/√(7²+24²)
PQ = | -14 -96 +10 | / √(49+576)
PQ = |-100| / √(625)
PQ = 100/25
PQ = 4 units
•So ,
Equation of PQ is 24x +7y + 20 = 0
&
Length of PQ is 4 units