Question

If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q $\left(\frac{5}{3},b\right)$, Then,

(a) $a=\frac{8}{3},b=\frac{2}{3}$

(b) $a=\frac{7}{3},b=0$

(c) $a=\frac{1}{3},b=1$

(d) $a=\frac{2}{3},b=\frac{1}{3}$

Answer 1

We have two points A (3,−4) and B (1, 2). There are two points P (a,−2) and Q which trisect the line segment joining A and B.

Now according to the section formula if any point P divides a line segment joining andin the ratio m: n internally than,

The point P is the point of trisection of the line segment AB. So, P divides AB in the ratio 1: 2

Now we will use section formula to find the co-ordinates of unknown point A as,

Equate the individual terms on both the sides. We get,

Similarly, the point Q is the point of trisection of the line segment AB. So, Q divides AB in the ratio 2: 1

Now we will use section formula to find the co-ordinates of unknown point A as,

Equate the individual terms on both the sides. We get,

So the answer is (b)