Vidaara.orgClass 10 · Mathematics
CodeVID-M10-20-AB-01
Locus Equidistant from Two Intersecting Lines — 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 intersecting lines is the:
- A.perpendicular bisector
- B.pair of angle bisectors
- C.circle
- D.midpoint
2.
The two angle bisectors are ___ to each other.
- A.parallel
- B.perpendicular
- C.equal
- D.coincident
3.
Each bisector bisects the ___ between the lines.
- A.length
- B.angle
- C.area
- D.distance
4.
A point on a bisector is equidistant from both:
- A.points
- B.lines
- C.circles
- D.axes
5.
The number of angle bisectors is:
- A.$1$
- B.$2$
- C.$3$
- D.$4$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Name the locus equidistant from two intersecting lines.
7.
How many such bisectors are there?
8.
What angle do the two bisectors make with each other?
9.
A point equidistant from two lines lies on the:
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Describe the locus of a point equidistant from two intersecting lines.
11.
Two roads cross. Describe the path equidistant from both roads.
12.
At what angle are the two angle bisectors of two intersecting lines inclined to each other?
13.
Is the locus one line or two?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Two straight lines intersect at $O$. Describe the complete locus of a point equidistant from both lines and state the relationship between its parts.
15.
Describe the locus of a point equidistant from two intersecting lines and also at a fixed distance from their point of intersection $O$.
Answer Key
Section A — Multiple Choice Questions
- (B) pair of angle bisectors
- (B) perpendicular
- (B) angle
- (B) lines
- (B) $2$
Section B — Short Answer (2 marks)
- The pair of angle bisectors.
- Two.
- $90^\circ$.
- Angle bisector.
Section C — Short Answer (3 marks)
- The pair of bisectors of the angles between them.
- The angle bisectors of the angles between them.
- $90^\circ$.
- Two (the angle bisectors).
Section D — Long Answer (5 marks)
- The pair of angle bisectors, which are perpendicular to each other.
- Up to $4$ points (where the angle bisectors meet a circle of that radius centred at $O$).
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