Calculate the distance between two points on the Cartesian plane, and apply it to identify triangle types and other shapes.
The distance between two points (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)²+(y₂−y₁)²], derived from the Pythagoras theorem.
Find the distance between (2,3) and (5,7).
√[(5−2)²+(7−3)²]=√[9+16]=√25=5
Find the distance between (0,0) and (6,8).
√[36+64]=√100=10
By computing distances between vertices, we can determine if a triangle is equilateral, isosceles, or right-angled, or if a quadrilateral is a square or rectangle.
Points A(0,0), B(4,0), C(4,3). Show this triangle is right-angled.
AB=4, BC=3, AC=√(16+9)=5; since 4²+3²=5², it's right-angled at B
Points A(1,1), B(4,1), C(4,5). Is triangle ABC isosceles?
AB=3, BC=4, AC=√(9+16)=5; all sides different, so it's scalene, not isosceles
1. Find the distance between (1,2) and (4,6).
2. Find the distance between (−3,4) and (0,0).
3. Points A(0,0), B(3,0), C(3,4). Show this triangle is right-angled.
4. Find the distance between (2,−3) and (2,5).
5. Points A(1,1), B(1,4), C(5,4), D(5,1). What shape is ABCD? (Check side lengths.)
From Rational & Irrational Numbers to the Distance Formula — the entire Class 9 Maths syllabus is done. Onwards to new challenges!
← Back to the full map