Find the point on the line 4 x + 7 y + 2 = 0 which is closest to the point ( − 1 , − 3 ) .

Question

Need answer ASAP. with work please. Thank you so much!

Answer 1

Shortest distance is measured on the perpendicular.

y = -4x / 7 - 2 / 7

y_perp = 7x / 4 + b

-3 = 7(-1) / 4 + b

-3 = -7/ 4 + b

-5 / 4 = b

y_perp = 7x / 4 - 5/ 4

To determine point on given line closest, determine the common solution to y and y_perp.