How to do question 24. a and b?

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Answer 1 · 2018-02-03T10:55:22

a) Equation of BC is $3 y - x = 22$ $color(blue)(3y - x = 22)$

b) Coordinates of $C (14, 12)$ $color(green)(C (14, 12)$

$A (4, 2), B (2, 8)$ $A (4,2), B (2,8)$

Equation of AC $y = x - 2$ $color(blue)(y = x - 2)$

a) To find equation of BC#

Slope of AB = (8-2) / (2 - 4) = -3#

Slope of BC = -1 / (-3) = 1/3#

Equation of BC

$y - 8 = (\frac{1}{3}) (x - 2)$ $y - 8 = (1/3) (x - 2)$

$3 y - 24 = x - 2$ $3y - 24 = x - 2$

Equation of BC is $3 y - x = 22$ $color(blue)(3y - x = 22)$

b) To find the coordinates of C.

This can be arrived at by solving equations of AC and BC.

Equation of AC $y - x = - 2$ $y - x = -2$ Eqn (1)

Equation of BC $3 y - x = 22$ $3y - x = 22$ Eqn (2)

Subtracting Eqn (1) from (2),

$3 y - y = 22 - (- 2)$ $3y - y = 22 - (-2)$

$y = \frac{24}{2} = 12$ $y = 24 / 2 = 12$

Substituting value of y in equation (1),

$12 - x = - 2$ $12 - x = -2$

$x = 12 + 2 = 14$ $x = 12 + 2 = 14$

Coordinates of $C (14, 12)$ $color(green)(C (14, 12)$