Question

04
The vertices of AABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and th
length of the altitude through A.​

Answer 1

Answer:

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 (x

1

​

,y

1

​

)&(x

2

​

,y

2

​

)=

x

2

​

−x

1

​

y

2

​

−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

2

​

in eq

n

(i), we get

m

1

​

=

(

2

1

​

)

−1

​

=−2

The equation of line passing through the point (x

1

​

,y

1

​

) with slope m is-

y−y

1

​

=m(x−x

1

​

)

∴ 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

Plz Mark me BRAINLEST

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Area of triangle = 20 sq unit

length of altitude= 40/√58