Area of a triangle from coordinates: Class 10 practice
Area = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Coordinates
The idea behind area of a triangle from coordinates
Area = ½|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. If the area is 0, the three points are collinear.
Step-by-step method
- Substitute the coordinates carefully.
- Take the absolute value and halve.
- Area 0 means collinear.
Worked example 1 (Basic)
Find the area of the triangle with vertices (6,-5), (0,4) and (2,1).
- ½|6(4 − 1) + 0(1 − -5) + 2(-5 − 4)|
- = 0
- Answer: 0 sq units
Worked example 2 (Standard)
Find the area of the triangle with vertices (-4,-1), (-5,-3) and (0,-5).
- ½|-4(-3 − -5) + -5(-5 − -1) + 0(-1 − -3)|
- = 6
- Answer: 6 sq units
Worked example 3 (Challenge)
Are (4,-4), (-6,-5) and (-16,-6) collinear? Use the area formula.
- ½|4(-5 − -6) + -6(-6 − -4) + -16(-4 − -5)|
- = 0
- Answer: Yes (area 0)
Common mistakes and misconceptions
- Dropping the absolute value
- Sign slips
Practice questions
- (Basic) Find the area of the triangle with vertices (0,2), (5,-3) and (6,6).
- (Basic) Find the area of the triangle with vertices (-4,3), (1,3) and (-1,-2).
- (Standard) Find the area of the triangle with vertices (-3,4), (2,3) and (-6,0).
- (Standard) Find the area of the triangle with vertices (0,6), (-4,-5) and (-6,6).
- (Challenge) Are (-2,6), (6,-4) and (22,-24) collinear? Use the area formula.
- (Challenge) Are (-5,0), (0,4) and (5,8) collinear? Use the area formula.
Answer key with full working
- Q1: ½|0(-3 − 6) + 5(6 − 2) + 6(2 − -3)| → = 25 → Answer: 25 sq units
- Q2: ½|-4(3 − -2) + 1(-2 − 3) + -1(3 − 3)| → = 12.5 → Answer: 12.5 sq units
- Q3: ½|-3(3 − 0) + 2(0 − 4) + -6(4 − 3)| → = 11.5 → Answer: 11.5 sq units
- Q4: ½|0(-5 − 6) + -4(6 − 6) + -6(6 − -5)| → = 33 → Answer: 33 sq units
- Q5: ½|-2(-4 − -24) + 6(-24 − 6) + 22(6 − -4)| → = 0 → Answer: Yes (area 0)
- Q6: ½|-5(4 − 8) + 0(8 − 0) + 5(0 − 4)| → = 0 → Answer: Yes (area 0)
Syllabus note
This skill is listed under "Coordinate Geometry" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is area of a triangle from coordinates in?
"Coordinate Geometry", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.