**Worksheet on Locus : **

Worksheet given in this section is much useful to the students who would like to practice problems on locus.

**Problem 1 :**

Draw point C on a piece of paper. Draw and describe the locus of all points on the paper that are e inches from c.

**Problem 2 :**

Points A and B lie in a plane. What is the locus of points in the plane that are equidistant from points A and B and are a distance of AB from B ?

**Problem 3 : **

Point P is in the interior of ∠ABC. What is the locus of points in the interior of ∠ABC that are equidistant from both sides of ∠ABC and 2 inches form P ? How does the location of P within ∠ABC affect the locus ?

**Problem 4 :**

We have the following readings of an earthquake from three seismographs.

(i) At A(-5, 5), the epicenter is 4 miles away.

(ii) At B(-4, -3.5), the epicenter is 5 miles away.

(iii) At C(1, 1.5), the epicenter is 7 miles away.

Where is the epicenter ?

**Problem 1 :**

Draw point C on a piece of paper. Draw and describe the locus of all points on the paper that are e inches from c.

**Solution : **

**Step 1 : **

Draw point C. Locate several points e inches
from C.

**Step 2 : **

Recognize a pattern: the points lie on a circle.

**Step 3 :**

Draw the circle using compass as shown below.

The locus of points on the paper that are e inches from C is a circle with center C and a radius of 3 inches.

**Problem 2 :**

Points A and B lie in a plane. What is the locus of points in the plane that are equidistant from points A and B and are a distance of AB from B ?

**Solution : **

The locus of all points that are equidistant from A and B is the perpendicular bisector of AB as shown below.

The locus of all points that are a distance of AB from B is the circle with center B and radius AB as shown below.

These loci intersect at D and E. So D and E are the locus of points that satisfy both conditions.

**Problem 3 : **

Point P is in the interior of ∠ABC. What is the locus of points in the interior of ∠ABC that are equidistant from both sides of ∠ABC and 2 inches form P ? How does the location of P within ∠ABC affect the locus ?

**Solution : **

The locus of points equidistant from both sides of ∠ABC is the angle bisector. The locus of points 2 inches form P is a circle. The intersection of the angle bisector and the circle depends on the location of P. The locus can be 2 points, 1 point, or 0 points.

**The locus is two points :**

**The locus is one point :**

**The locus is zero points :**

**Problem 4 :**

We have the following readings of an earthquake from three seismographs.

(i) At A(-5, 5), the epicenter is 4 miles away.

(ii) At B(-4, -3.5), the epicenter is 5 miles away.

(iii) At C(1, 1.5), the epicenter is 7 miles away.

Where is the epicenter ?

**Solution : **

Each seismograph gives us a locus that is a circle.

So, we have

Circle A has center (-5, 5) and radius 4

Circle B has center (-4, -3.5) and radius 5

Circle C has center (1, 1.5) and radius 7

Draw the three circles in a coordinate plane. The point of intersection of the three circles is the epicenter.

In the diagram above, three circles intersect at (-6, 1).

The epicenter is at about (-6, 1).

After having gone through the stuff given above, we hope that the students would have understood, "Worksheet on Locus".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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