SSC CGL 2025 Tier-I · 22 September 2025, Shift 1 · Quantitative Aptitude · Question 18 of 98

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What is the length of the segment joining (1,2) and (4,6)?

(a)5
(b)2
(c)4
(d)3

Answer

Why

Correct — A. Use the distance formula: d = √((x₂ − x₁)² + (y₂ − y₁)²).

Horizontal gap: 4 − 1 = 3
Vertical gap: 6 − 2 = 4
Square and add: 3² + 4² = 9 + 16 = 25

Square root: d = √25 = 5 → option (a)

Why the others are wrong

(b)
2 — 2 is shorter than both gaps. The segment is the hypotenuse of a right triangle with legs 3 and 4, and a hypotenuse is always longer than either leg.
(c)
4 — 4 is the vertical gap alone, 6 − 2. That is one leg of the right triangle, and the slanted segment joining the points is longer than either leg.
(d)
3 — 3 is the horizontal gap alone, 4 − 1. Stopping there drops the rise of 4 units, and both gaps go into the formula as squares.

Concept

The distance formula is Pythagoras on a grid. Joining (x₁, y₁) to (x₂, y₂), the horizontal gap and the vertical gap are the two legs of a right triangle, and the segment is its hypotenuse.

So d² = (x₂ − x₁)² + (y₂ − y₁)². The order of subtraction does not matter, because each gap is squared.

Here the legs are 3 and 4, the 3-4-5 triple, so the length is a whole number.

The three wrong options are 2, 4 and 3, none longer than the longer leg. Knowing that a hypotenuse is longer than both legs settles the item before any squaring.

Key facts

Distance between (x₁, y₁) and (x₂, y₂) = √((x₂ − x₁)² + (y₂ − y₁)²).
The horizontal and vertical gaps are the legs of a right triangle, and the segment is its hypotenuse.
3, 4, 5 is a Pythagorean triple: 3² + 4² = 5².

Study next

Midpoint of a segment: ((x₁ + x₂)⁄2, (y₁ + y₂)⁄2)Section formula: the point dividing a segment in a given ratioOther Pythagorean triples: 5-12-13, 8-15-17, 7-24-25

Common traps

Reporting one of the gaps, 3 or 4, as the length instead of combining both.
Squaring and adding to 25 but forgetting the square root.

Coordinate geometry also appears on 21 Sep 2025, 16:00, Quant Q.23, where P is equidistant from A(0, 0), B(4, 0) and C(0, 3): the same 3-4-5 triangle, and the keyed point (2, 1.5) is the midpoint of the 5-unit side BC.

18 Sep 2025, 09:00, Quant Q.16 asks for the midpoint of (3,4) and (7,8) instead of the length.

Related PYQs

No directly related past PYQ was found.

Topic: Graphs of Linear Equations — all 27 SSC CGL questions on it, every solved shift.