NCERT Solutions for Class 9th Maths Chapter 1 Think and Reflect — Distance Between Two Points in the 2-D Plane
Book page 9 Updated on2026-09-08
Q1.
In moving from A (3, 4) to D (7, 1), what distance has been covered along the x-axis? What about the distance along the y-axis?
Answer
Along the x-axis: 7 − 3 = 4 units (to the right) Along the y-axis: 1 − 4 = −3, that is 3 units downwards
In Fig. 1.7 these two shifts appear as the segments CD = 4 and AC = 3, where C = (3, 1).
Why it happens: The x-coordinate records position along the horizontal direction only, so the change in x measures the horizontal part of the journey and nothing else. Likewise for y. The minus sign in 1 − 4 is information, not an error — it says the movement was downwards. For a length we take the size, 3 units.
Q2.
Can these distances help you find the distance AD?
Answer
Yes. The two shifts are the legs of a right triangle whose hypotenuse is AD.
Turning point C = (3, 1) AC is vertical (x = 3 throughout) and CD is horizontal (y = 1 throughout) → ∡ACD = 90°
By the Baudhāyana–Pythagoras Theorem:
AD² = AC² + CD² = 3² + 4² = 9 + 16 = 25
AD = 5 units
Why it happens: A horizontal line and a vertical line always meet at a right angle — that is how the two axes were set up in the first place. So splitting any journey into a horizontal stage and a vertical stage automatically manufactures a right triangle, and the theorem is always available. This single observation is what turns geometry into algebra: AD = √((x₂ − x₁)² + (y₂ − y₁)²).
Tip: It makes no difference which point you start from. Going from D to A the shifts are −4 and +3, and squaring turns both signs into the same positive numbers: (−4)² + 3² = 25. Distance has no direction.