from the point p(-2,4) if PQ is drawn perpendicular to line 7x-24y+10=0,find the eqaution of the lin PQ . also determine the length of PQ

7y+24x = -12

Step-by-step explanation:

Equation of line PQ in point slope form is expressed as;

y -y0 = m(x-x0)

m is the slope of {Q

(x0, y0) is the point on the line

Given the line 7x-24y+10=0

Get the slope

-24y = -7x -10

y = -7/-24 x - 10/-24

y = 7/24 x + 5/12

Slope = 7/24

Slope of the line PQ perpendicular to it = -24/7

Substitute m = -24/7 and (-2, 4) into the formula;

y - 4 = -24/7(x+2)

7(y-4) = -24(x+2)

7y - 28 = -24x-48

7y + 24x = -40 + 28

7y+24x = -12

This gives the equation of the line PQ