Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x ?
Ans:
Step 1: Now, by section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be given by:
P (X,Y) =
here, point divides the line in ratio of m1 : m2
Step 2: Now if the given points A (3, -5) and B(- 1, 6) are divided in the ratio of m : n, then:
coordinates of dividing point (x, y) =
=
Step 3: Next, since this point lies on line y = x, this point will satisfy the equation
∴
∴ 6 m – 5 n = 3 n – m
∴ 7 m = 8 n
∴ m : n = 8 : 7
Therefore, the line segment divides the line in ratio of 8:7.
Check: Let’s plot the points on the graph:
Here, we can see that line x = y is cutting line AB in a ratio where m is almost equal to n. hence our answer is correct.
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