Area of a triangle from coordinates MCQs

Q1. If the area of a triangle from three points is zero, the points are (NCERT):

• A.a right triangle
• B.the same point
• C.equidistant
• D.collinear

Answer: D. collinear

Q2. If three points give area 0 with one unknown coordinate, we (NCERT):

• A.guess it
• B.cannot find it
• C.conclude no solution
• D.solve for the unknown

Answer: D. solve for the unknown

Quick parse - a typical math numerical. The data on the table: 0. We are after the quantity the stem asks for. Tool of choice - hence the required answer = solve for the unknown. Rearrange it for the unknown before substituting. Common-sense check: set up the relation specified by the stem (formula / theorem from the relevant Class-10 chapter) and substitute the listed numerical data. Lock in option D) solve for the unknown. Trap-watch: option A) 'guess it' doesn't hold - It is found exactly; option B) 'cannot find it' is incorrect: Area=0 gives an equation.

Q3. Find the area of the triangle with vertices (0, 0), (4, 0), (0, 6).

• A.12 sq units
• B.6 sq units
• C.24 sq units
• D.13 sq units

Answer: A. 12 sq units

Spot-the-setup - a typical math numerical. The data on the table: 0, 0, 4, 0, 0. We are after Find the area of the triangle with vertices (0, 0), (4, 0), (0, 6). Tool of choice - area = (1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|. Rearrange it for the unknown before substituting. Numbers in: area = (1/2)|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)| → = (1/2)*|0(-6)+4(6)+0(0)| = (1/2)*|24| = 12. Common-sense check: three-step shoelace chain. Lock in option A) 12 sq units. Trap-watch: option B) '6 sq units' is incorrect: Don't halve twice; option C) '24 sq units' doesn't hold - Divide by 2 in the shoelace formula.