Vidaara.orgClass 10 · Mathematics
CodeVID-M10-20-LB-01
Locus Equidistant from Two Points — 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 locus equidistant from two fixed points is the:
- A.circle
- B.perpendicular bisector
- C.angle bisector
- D.midpoint
2.
This locus is a:
- A.curve
- B.straight line
- C.circle
- D.point
3.
It passes through the ___ of the segment.
- A.endpoint
- B.midpoint
- C.centre
- D.origin
4.
It is ___ to the segment joining the two points.
- A.parallel
- B.perpendicular
- C.equal
- D.tangent
5.
Every point on it is equidistant from the two:
- A.lines
- B.fixed points
- C.circles
- D.axes
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Name the locus equidistant from $A$ and $B$.
7.
Through which point does it pass?
8.
Is it parallel or perpendicular to $AB$?
9.
Is the perpendicular bisector a line or a curve?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Describe the locus of a point equidistant from two points $A$ and $B$.
11.
Find the equation of the locus equidistant from $(0,0)$ and $(4,0)$.
12.
Where and at what angle does the perpendicular bisector meet $AB$?
13.
Find the locus equidistant from $(0,0)$ and $(0,6)$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the equation of the locus of a point equidistant from $A(1,2)$ and $B(5,6)$.
15.
Two points $A$ and $B$ are $8$ cm apart. Describe the locus of a point equidistant from $A$ and $B$ and state its relation to the midpoint of $AB$.
Answer Key
Section A — Multiple Choice Questions
- (B) perpendicular bisector
- (B) straight line
- (B) midpoint
- (B) perpendicular
- (B) fixed points
Section B — Short Answer (2 marks)
- The perpendicular bisector of $AB$.
- The midpoint of $AB$.
- Perpendicular.
- A straight line.
Section C — Short Answer (3 marks)
- The perpendicular bisector of $AB$.
- $x=2$.
- At its midpoint, at $90^\circ$.
- $y=3$.
Section D — Long Answer (5 marks)
- $x+y=7$.
- The perpendicular bisector of $AB$, passing through its midpoint at $90^\circ$.
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