Math, asked by mukesh9807989, 1 year ago

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. ​

Attachments:

Answers

Answered by AnkitaSahni
15

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

Similar questions