Distance between the points (−3, 5) and (1, 5).

Class 10Coordinate GeometryGeometry — Coordinates

Step-by-Step Solution

y

-coordinates are equal, so the segment is horizontal. Distance = |

1 - (- 3) ∣ = 4

Answer: B) 4

Key idea: Distance formula

**Distance** between two points P

(x

₁,

y

₁) and Q

(x

₂,

y

₂):

**PQ =

(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

**

This is just the Pythagoras theorem applied to the right triangle formed with horizontal and vertical legs.

**Example**: Distance between (3, 4) and (7, 1).
=

(7 - 3)^{2} + (1 - 4)^{2} = 16 + 9 = 25 = 5

.

**Special distance from origin**: distance of

(x, y)

from (0, 0) is

x^{2} + y^{2}

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