Question

find the equation of the altitude of the triangle whose vertices are A(7,-1) ;B(-2,8);c(1,2)​

Answer 1

Answer:

The area of the triangle would be 12unit sq.

Step-by-step explanation:

Answer 2

The required equation of the altitude is $x-2y-9=0$.

Step-by-step explanation:

Consider the provided information.

First find the slope of BC by using the formula: $m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2-8}{1-(-2)}$

$m=\frac{-6}{3}=-2$

AD is perpendicular to BC therefore the slope of AD is negative reciprocal of slope of BC.

Negative reciprocal of -2 is $\frac{1}{2}$

Hence, the slope of AD is $\frac{1}{2}$.

Now find the equation of line using two point slope form:

$(y-y_1)=m(x-x_1)$

Substitute y₁ = -1 and x₁ = 7 in above formula.

$(y+1)=\frac{1}{2}(x-7)$

$2y+2=x-7$

$2y=x-9$

$x-2y-9=0$

Hence, the required equation of the altitude is $x-2y-9=0$.

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