Question

6) If point P ( 1 , 1 ) divide segment joining point A and point B ( -1 , -1 )

in the ratio 5 : 2 then the coordinates of A are ---------

A)( 3 ,3 ) B)( 6, 6 ) C)(2, 2 ) D)(1, 1​

Answer 1

Answer:

Step-by-step explanation:

Given:

x + y = 12

y = 12 – x -----------1

Also given:

10y + x - 10x – y = 18

9y – 9x = 18

y – x = 2 -------------2

Substitute the value of y from eqn 1 in eqn 2

12 – x – x = 2

12 – 2x = 2

2x = 10

x = 5

Therefore, y = 12 – x = 12 – 5 = 7

Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57

Answer 2

Answer:

B) (6, 6)

Step-by-step explanation:

Let the coordinates of A be (x1, y1)

5 : 2

----------------- -----------------

A(x, y) P(1, 1) B(-1, -1)

take P(1, 1) as x and y

$x = \frac{m_{1}x _{2} + m_{2}x _{1}}{m_{1} + m_{2}} \\ 1 = \frac{5 \times ( - 1) + 2x}{5 + 2} \\ 1 = \frac{ - 5 + 2x}{7} \\ 7 = - 5 + 2x \\ 2x = 12 \\ x = 6 \\ y = \frac{m_{1}y_{2} + m_{2}y _{1}}{m_{1} + m_{2}} \\ 1 = \frac{ - 5 + 2y}{7} \\ 7 = - 5 + 2y \\ 2y = 12 \\ y = 6$

therefore the coordinates of A(x1+y1) =(6,6)