Question

The point (8,4) divides the line segment joining (5,-2) and (9,6) in the ratio a) - 3:1 b) 3:1 c) - 1:3 ​

Answer 1

Answer:

The ratio is (b) 3:1

Step-by-step explanation:

We know that if a point (x,y) divides a line segment joining (x1,y1) and (X2,y2) in the ratio m:n then, (x,y) ={ (mx2 + nx1)/(m+n) , (my2 + ny1)/(m+n)}

Let, the point (8,4) divides the line segment joining (5,-2) and (9,6) in the ratio m:n

Hence, 8 = (m×9 + n×5 )/(m+n)

=> 8m + 8n = 9m + 5n

=> 9m-8m = 8n-5n

=> m = 3n

=> m/n = 3

=> m:n = 3:1

Hence, the point (8,4) divides the line segment joining (5,-2) and (9,6) in the ratio 3:1