# CBSE Class 10 Math Question Paper 2016 | Q6

###### Board Paper Solution | 2 Mark | Coordinate Geometry | Section Formula

The given question is a medium difficulty 2-mark question that appeared in the CBSE Class 10 Math 2016 board paper. Chapter : Coordinate Geometry. Concept: Computing the ratio in which two points divide a line segment and then applying the section formula to compute the coordinates of those two points.

Question 6: Let P and Q be the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4) such that P is nearer to A. Find the coordinates of P and Q.

## NCERT Solution to Class 10 Maths

### Explanatory Answer | CBSE 2016 Maths Paper Q6

Because points P and Q trisect the line segment AB, P and Q will divide AB into 3 equal parts such that AP = PQ = QB.
Hence, point P divides AB in the ratio 1 : 2

##### Step 1: Compute Coordinates of Point P

∴ X coordinate of P = $$frac{\text{1$-7$ + 2(2)}}{$text{1 + 2}}) = $\frac{\text{-3}}{\text{3}}$ = -1 Y coordinate of P = $\frac{\text{1$4$ + 2(-2)}}{$text{1 + 2}}) = 0 Coordinates of point P are$-1, 0)

##### Step 2: Compute Coordinates of Point Q

Point Q divides AB in the ratio 2 : 1
∴ X coordinate of Q = $$frac{\text{2$-7$ + 1(2)}}{$text{1 + 2}}) = -4 Y coordinate of Q = $\frac{\text{2$4$ + 1(-2)}}{$text{1 + 2}}) = 2 Coordinates of point Q are$-4, 2)

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