Question

The line segment AB is divided at P(1,1) internally in the ratio 5:2 and co ordinates of point B are (-1,-1) find the co ordinates of point A​

Answer 1

Step-by-step explanation:

P ( 1, 1 )

B (-1 , -1 )

Let A ( x,y)

P ( 5 (-1) + 2x /7 5 (-1) + 2y / 7

-5 + 2x / 7 = 1

2x = 7+5

x= 6

and

-5 +2y /7 = 1

2y = 7+5

y= 6

Point A have coordinates ( 6,6)

Hope it helps you

Answer 2

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GIVEN THAT:-

$&#10155$ The line segment AB is divided at P(1,1) internally in the ratio 5:2 and co ordinates of point B are (-1,-1)

FORMULA:-

$&#10155$ If a line segment AB { A ( x1,y1) and B ( x2,y2) } is divided at P point(x,y) internally in the ratio of m:n then the co ordinator of point p is

$&#10152 \: \: x = \: \frac{n \times x1 + m \times x2}{m + n} \\ \\ &#10152 \: \: y = \frac{n \times y1 + m \times y2}{m + n}$

SOLUTION;

$&#10155$ Line segment AB

coordinates of P = (1,1)

Ratio = 5:2

coordinates of Point B = (–1,–1)

Let Coordinate of point A = (x,y)

using the formula

x ordinate of point A

$\implies \: \: 1 = \frac{2 \times x + 5( - 1)}{5 + 2} \\ \\ \implies \: \: 2x - 5 = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: 2x = 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: x = \frac{\cancel{12}}{\cancel2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: x = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

y ordinate of point A

$\implies \: \: 1 = \frac{2 \times y + 5( - 1)}{5 + 2} \\ \\ \implies \: \: 2y - 5 = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: 2y = 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: y = \frac{\cancel{12}}{\cancel2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: \: y = 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now the coordinate of point A = (6,6)