Question

2. In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b. (1) P(-3, 7), Q(1, -4), a: b = 2 : 1 ​

Answer 1

Step-by-step explanation:

$points \: \: \: p( - 3,7) \: and \: q(1, - 4) \\ ratio \: (a : b) = (2 : 1) = (m_{1} : m_{2})\\ by \: section \: formula \\ coordinates \: of \: point \: \: \: p \: = ( \frac{x_{2}m_{1} + x_{1}m_{2} }{m_{1} + m_{2}},\frac{y_{2}m_{1} + y_{1}m_{2} }{m_{1} + m_{2}}) \\ coordinates \: of \: point \: \: \: p \: = ( \frac{1 \times 2 + ( - 3) \times 1}{2 + 1}, \frac{( - 4) \times 2 + 7 \times 1}{2 + 1} ) \\ coordinates \: of \: point \: \: \: p = ( \frac{2 - 3}{3} , \frac{ - 8 + 7}{3} ) \\ = ( \frac{ - 1}{3} , \frac{ - 1}{3} )$

Answer 2

Answer:

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let the coordinates of point A be (x, y).

P(-2, -5), Q(4, 3), a : b = 3 : 4

Therefore,

x=

3+4

3×4+4×(−2)

=

7

12−8

=

7

4

y=

3+4

3×3+4×(−5)

=

3

9−20

=

7

−11

(x,y)=(

7

4

,

7

−11

)