Question

Copy the points $F$, $T$ and $P$ from the diagram on page 2. If you lay your paper over the page, you can see through the paper will enough to get the points?

1. Draw a line to indicate all points equidistant from $F$and $T$.
2. Draw a circle to indicate points 6 cm from $P$. If you don’t have a compass, draw as well as you can freehand.
3. How many points are equidistant from $F$ and $T$, and are also 6 cm from role="math" localid="1648732740314" $P$?

Short answer

a.

b.

c. The figure below represents the count of points, which is 2, with the same distance from the points $F$ and $T$ and a distance of 6 cm from the point $P$.

Step-by-step solution

Part a. Step 1. Make the points P, F and T.

Part a. Step 2. Take the help of a ruler to draw the line.

Take the ruler from the side of the centimeter and use its side to make a point that has the same distance from $F$ and $T$ and ensure that the position of the point is between $F$ and $T$. After that, use that point to make a vertical line.

Part a. Step 3. Conclude by performing a checking.

Use a ruler and measure that the distance of the vertical line is equal between points $F$ and $T$. The distance is equal, which means that the points present on the vertical line have equal distance from the points $F$ and $T$.

Part b. Step 1. Make the points P, F and T.

Part b. Step 2. Draw the required circle.

Take $P$ as the center point and make a circle having a radius of 6 cm. This can be done by opening the compass at the measurement of 6 cm and then make a rotation of 360 degrees by putting the needle of the compass at $P$.

Part b. Step 3. Conclude by performing a checking.

Use a ruler and measure that the distance of the point $P$ from the surface of the circle is 6 cm. The distance is 6 cm which means that the radius of the circle is represented by 6 cm.

Part c. Step 1. Make the points P, F and T.

Part c. Step 2. Make a vertical line that contains all the points having the same distance from the points F and T.

Take the ruler from the side of the centimeter and use its side to make a point that has the same distance from $F$ and $T$ and the position of the point is between $F$ and $T$. After that, use that point to make a vertical line.

Part c. Step 3. Draw the circle with a radius of 6 cm by taking the point P as its center point.

Take $P$ as the center point and make a circle having a radius of 6 cm. This can be done by opening the compass at the measurement of 6 cm and then making a rotation of 360 degrees by putting the needle of the compass at $P$. After that, mark the points where the circle is intersecting with the vertical line.

Part c. Step 4. Conclude by performing a checking.

Use a ruler and measure that the distance of the point $P$ from the points where the circle intersects the vertical line is 6 cm. After that, measure that each intersecting point has the same distance from both the points $F$ and $T$. The distance is equal from $F$ and $T$ and 6 cm from $P$, which means that the distance between point P and the intersecting points is represented by 6 cm. Also, each point has the same distance from both the points $F$ and $T$.