Question

4. n. Write down the equation of the line whose gradient is and which passes through p. where p diovides the line segment joining A(2,-4) and (-5,9) in the ratio 3:4​

Answer 1

Given, P divides the line segment joining the points A(−2,6) and B(3,−4) in the ratio 2:3

So, the co-ordinates of P will be

x=

(m

1

+m

2

)

(m

1

x

2

+m

2

x

1

)

=

(2+3)

(2×3+3×(−2))

=

5

(6−6)

=

5

0

=0

y=

(2+3)

(2×(−4)+3×(6))

5

(−8+18)

=

5

10

=2

Hence, the co-ordinates of P are (0,2)

Now, the slope (m) of the line passing through (0,2) is

2

3

Thus, the equation will be

y−y

1

=m(x−x

1

)

y−2=

2

3

(x−0)

2y−4=3x

⇒3x−2y+4=0