← Back to chapter
Vidaara.orgClass 10 · Mathematics
CodeVID-M10-06-CT
Coordinate Geometry — Full Chapter Test
Chapter: Coordinate Geometry
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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 distance between two points is:
  • A.$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  • B.$(x_2-x_1)$
  • C.$x_1x_2+y_1y_2$
  • D.$x_2+y_2$
2.
The internal section formula for $x$ is:
  • A.$\tfrac{mx_2+nx_1}{m+n}$
  • B.$\tfrac{x_1+x_2}{2}$
  • C.$mx_1+nx_2$
  • D.$\tfrac{mx_1-nx_2}{m-n}$
3.
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.$y_1+y_2+y_3$
4.
The distance between $(0,0)$ and $(3,4)$ is:
  • A.$7$
  • B.$5$
  • C.$1$
  • D.$25$
5.
The midpoint formula gives:
  • A.$\left(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2}\right)$
  • B.$(x_1+x_2,y_1+y_2)$
  • C.$(x_1x_2,y_1y_2)$
  • D.$(0,0)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the distance between $(1,2)$ and $(4,6)$.
7.
Find the midpoint of $(1,2)$ and $(5,6)$.
8.
Find the area of the triangle $(0,0),(4,0),(0,3)$.
9.
Find the distance of $(6,8)$ from the origin.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Show that $(3,0),(6,4),(-1,3)$ are the vertices of a right triangle.
11.
Find the point dividing $(4,-3)$ and $(8,5)$ in the ratio $3:1$.
12.
Find the area of the triangle with vertices $(1,2),(4,5),(3,8)$.
13.
Find the point on the x-axis equidistant from $(2,-5)$ and $(-2,9)$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Show that $(1,7),(4,2),(-1,-1),(-4,4)$ are the vertices of a square.
15.
Find the ratio in which the line $2x+y-4=0$ divides the segment joining $A(2,-2)$ and $B(3,7)$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
  2. (A) $\tfrac{mx_2+nx_1}{m+n}$
  3. (A) $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$
  4. (B) $5$
  5. (A) $\left(\tfrac{x_1+x_2}{2},\tfrac{y_1+y_2}{2}\right)$
Section B — Short Answer (2 marks)
  1. $5$.
  2. $(3,4)$.
  3. $6$ sq units.
  4. $10$.
Section C — Short Answer (3 marks)
  1. Right-angled ($AB^2+AC^2=BC^2$).
  2. $(7,3)$.
  3. $6$ sq units.
  4. $\left(-\tfrac72,0\right)$.
Section D — Long Answer (5 marks)
  1. A square (all sides $\sqrt{34}$, equal diagonals).
  2. $2:9$.
Generated by Vidaara.org · Assignment VID-M10-06-CT · vidaara.org