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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-06-ARE-01
Area, Midpoint & Reflection — Assignment
Chapter: Coordinate Geometry
Topic: Area of Triangle, Midpoint and Reflection of Points
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The triangle-area formula is $\tfrac12|\dots|$ of:
  • A.$x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$
  • B.$x_1+x_2+x_3$
  • C.$x_1y_1+x_2y_2+x_3y_3$
  • D.$y_1+y_2+y_3$
2.
Three points are collinear if the area is:
  • A.$1$
  • B.$0$
  • C.$\tfrac12$
  • D.negative
3.
The centroid is:
  • A.$\left(\tfrac{x_1+x_2+x_3}{3},\tfrac{y_1+y_2+y_3}{3}\right)$
  • B.a midpoint
  • C.$(0,0)$
  • D.a vertex
4.
The reflection of $(3,5)$ in the x-axis is:
  • A.$(3,-5)$
  • B.$(-3,5)$
  • C.$(5,3)$
  • D.$(-3,-5)$
5.
The reflection of $(3,5)$ in the y-axis is:
  • A.$(3,-5)$
  • B.$(-3,5)$
  • C.$(5,3)$
  • D.$(-3,-5)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area of the triangle $(0,0),(4,0),(0,3)$.
7.
Are $(1,1),(2,2),(3,3)$ collinear?
8.
Find the centroid of $(0,0),(6,0),(0,9)$.
9.
Reflect $(2,-4)$ in the x-axis.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the area of the triangle with vertices $(1,2),(4,5),(3,8)$.
11.
Find $k$ if $(2,3),(4,k),(6,-3)$ are collinear.
12.
Find the centroid of the triangle $(3,-5),(-7,4),(10,-2)$.
13.
Reflect $(-3,7)$ in (i) the x-axis and (ii) the y-axis.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the area of the quadrilateral with vertices $(-4,-2),(-3,-5),(3,-2),(2,3)$.
15.
If $A(x,y),B(3,6),C(-3,4)$ are collinear, show that $x-3y+15=0$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$
  2. (B) $0$
  3. (A) $\left(\tfrac{x_1+x_2+x_3}{3},\tfrac{y_1+y_2+y_3}{3}\right)$
  4. (A) $(3,-5)$
  5. (B) $(-3,5)$
Section B — Short Answer (2 marks)
  1. $6$ sq units.
  2. Yes.
  3. $(2,3)$.
  4. $(2,4)$.
Section C — Short Answer (3 marks)
  1. $6$ sq units.
  2. $k=0$.
  3. $(2,-1)$.
  4. (i) $(-3,-7)$; (ii) $(3,7)$.
Section D — Long Answer (5 marks)
  1. $28$ sq units.
  2. $x-3y+15=0$.
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