Maths · Coordinate geometry · chapter 7 of 14

Class 10 Maths Chapter 7: Coordinate Geometry case study question with answers

One case-based question of the kind the board asks in Section E: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
The planning office of a hill town in Uttarakhand draws its map on a grid in which one unit is 1 km. The x-axis runs along the railway line and the y-axis along the river. The health centre is at H(−2, −3) and the new school at S(10, 13), as shown in the figure. A straight road HS is to be built between them, with a water tank at the middle of the road and other stops along it. The office wants the length of the road and the positions of the stops before work begins.
xy O 4 8 12 4 8 12 H(−2, −3) S(10, 13)
Part 1 · 1 mark
The length of the road HS is
Show answer

Answer: (b) 20 km

HS = √(12² + 16²) = √400 = 20 km. (28 adds the gaps; 2√41 = √164 adds the coordinates instead of subtracting them.)

Part 2 · 1 mark
The water tank, at the middle of the road, is at
Show answer

Answer: (b) (4, 5)

Mid-point = ((−2 + 10)/2, (−3 + 13)/2) = (4, 5). (6, 8) halves the differences instead of the sums.

Part 3 · 2 marks
A bus stop B is built on the road so that HB : BS = 3 : 1. Find the coordinates of B.
Answer and marking scheme

B = ((3 × 10 + 1 × (−2))/4, (3 × 13 + 1 × (−3))/4) = (28/4, 36/4) = (7, 9).

  • applies the section formula with m₁ = 3, m₂ = 1 (1)
  • B = (7, 9) (1)
Or
A tea stall T is set up on the road 5 km from the health centre. Find the coordinates of T.
Answer and marking scheme

HT = 5 km and HS = 20 km, so HT = (1/4)HS and HT : TS = 1 : 3 (the ratio of the parts, not 1 : 4). T = ((1 × 10 + 3 × (−2))/4, (1 × 13 + 3 × (−3))/4) = (1, 1).

  • HT : TS = 1 : 3 from HT = (1/4)HS (1)
  • T = (1, 1) (1)
Take the free Class 10 Maths testSee the Class 10 flashcards

← Chapter 6: TrianglesChapter 8: Introduction to Trigonometry →