Vidaara.orgClass 10 · Mathematics
CodeVID-M10-06-DIS-01
Distance Formula — Assignment
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 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 distance between $(0,0)$ and $(3,4)$ is:
- A.$7$
- B.$5$
- C.$1$
- D.$25$
3.
The distance from the origin to $(5,12)$ is:
- A.$12$
- B.$13$
- C.$17$
- D.$5$
4.
The distance between $(2,3)$ and $(2,7)$ is:
- A.$2$
- B.$4$
- C.$5$
- D.$\sqrt5$
5.
The distance between $(a,0)$ and $(0,a)$ is:
- A.$a$
- B.$a\sqrt2$
- C.$2a$
- D.$0$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the distance between $(1,2)$ and $(4,6)$.
7.
Find the distance of $(6,8)$ from the origin.
8.
Find the distance between $(-1,-1)$ and $(2,3)$.
9.
Find the distance between $(3,0)$ and $(0,4)$.
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 on the x-axis equidistant from $(2,-5)$ and $(-2,9)$.
12.
Find the distance between $(a\cos\theta,a\sin\theta)$ and the origin.
13.
Show that $(1,5),(2,3),(-2,-11)$ are not collinear.
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 point on the y-axis equidistant from $A(6,5)$ and $B(-4,3)$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- (B) $5$
- (B) $13$
- (B) $4$
- (B) $a\sqrt2$
Section B — Short Answer (2 marks)
- $5$.
- $10$.
- $5$.
- $5$.
Section C — Short Answer (3 marks)
- Right-angled ($AB^2+AC^2=BC^2$).
- $\left(-\tfrac72,0\right)$.
- $a$.
- Not collinear (sum of two distances $\ne$ third).
Section D — Long Answer (5 marks)
- A square (all sides $\sqrt{34}$, equal diagonals).
- $(0,9)$.
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