Find the coordinates of the foot of perpendicular drawn from the point (2,3) to the line 3x-4y+7=0?

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Answer 1 · 2018-01-22T12:50:13

Coordinates of the foot of the perpendicular

$B (\frac{47}{25}, \frac{79}{25})$ $color(green)(B (47/25, 79/25))$

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To find the Slope of the line CD $3 x - 4 y + 7 = 0$ $3x - 4y + 7 = 0$ Eqn (1)

$y = (\frac{3}{4}) x + \frac{7}{4})$ $y = (3/4)x + 7/4)$

$m = (\frac{3}{4})$ $m = (3/4)$

Slope of line AB perpendicular to the above line segment CD is

$m 1 = - \frac{1}{m} = - \frac{4}{3}$ $m1 = -1/m = -4/3$

Equation of the perpendicular line AB passing through point (2,3) is

$y - 3 = - (\frac{4}{3}) (x - 2)$ $y - 3 = -(4/3) (x - 2)$

$3 y + 4 x = 17$ $3y + 4x = 17$ . Eqn (2)

Solving Eqns (1), (2) we get the foot of the perpendicular B drawn from A (2,3)

$B (\frac{47}{25}, \frac{79}{25})$ $color(green)(B (47/25, 79/25))$