Question

30. Find the length of the median through vertex A of A ABC whose vertices are A (5,2).
B (4.7) and C ( 17.-4).
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Answer 1

Answer:

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,y1)&

(x2 ,y2)= x2 −x 1 y2 −y 1

∴ Slope of BC joining B(1,1)&C(−1,0)=

−1−1 0−1 = −2

−1 = 21

On substituting the value of m

2 in eq n

(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−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