Find the coordinates of the points which trisect the line segment joining the points P(4,2, – 6) and Q(10, – 16,6).

# Find the coordinates of the points which trisect the line segment joining the points P(4,2, - 6) and Q(10, - 16,6).

1. A

(6, - 4, - 2), (8, - 10, 2)

2. B

(6, 4, - 2), (8, - 10, 2)

3. C

(6, - 4, - 2), (8, 10, 2)

4. D

None of the above

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Let the point R1, trisects the line PQ i.e., it divides the line in the ratio 1:2

$\begin{array}{l}⇒{\mathrm{R}}_{1}=\left[\frac{1×10+2×4}{1+2},\frac{1×\left(-16\right)+2×2}{1+2},\frac{1×6+2×\left(-6\right)}{1+2}\right]\\ =\left(\frac{10+8}{3},\frac{-16+4}{3},\frac{6-12}{3}\right)=\left(\frac{18}{3},\frac{-12}{3},\frac{-6}{3}\right)\\ =\left(6,-4,-2\right)\end{array}$

Again, let the point R2 divides PQ internally in the ratio 2: 1. Then,

Hence, required points are (6,-4, - 2) and (8, - 10,2).

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)