Question

The vertices of a
triangle are AC14)
B (2,3) C (1,6)
find equation of
altitude of triangle ABC​

Answer 1

Step-by-step explanation:

Solution:-

Let ABC be the triangle with vertices A(2,−2),B(1,1) and C(−1,0)&AD be the altitude of △ABC drawn from A.

Let m 1&m 2 be the slope of line AD and BC respectively.

Now, AD⊥BC

∴m 1 ×m 2 =−1

⇒m 1 =m 2−1 ⟶(i)

Slope of line BC-

Slope of a line joining points

( X1 ,y 1 )&(x 2 ,y2 )=x 2−x 1 ( y2−y 1)

∴ Slope of BC joining B(1,1)&C(−1,0)=

−1−1 / 0−1 = −2−1/ = 2- 1

On substituting the value of m

2in eqn(i), we get

m1 = (21 −1 =−2

The equation of line passing through the point (x1 ,y 1) with slope m is-

y−y 1=m(x−x1)

∴ Equation of altitude AD passing through A(2,−2) with slope 2 is-

y−(−2)=−2×(x−2)

⇒y+2=−2x+4

⇒y=−2x+2

⇒y=−2x+2

⇒y=−2x+2

Answer

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