Two mobile phone masts P and Q are 30 km apart. Mast P has a radius of 20 km and Mast Q has a radius of 15km. a. Draw the locus of points covered by these two masts. Remember to give your scale. (3 marks) b. Label the points where the two circles meet as L and M and draw lines PL, LQ, QM and MP. (1 mark) c. What is the name given to the quadrilateral PLQM? (1 mark) d. Shade in the locus of points that is covered by both masts
To answer these questions, I'll guide you through the process step by step.
a. To draw the locus of points covered by the two mobile phone masts P and Q, we'll start by drawing two circles representing the coverage areas of each mast. The center of mast P will be labeled as P and the center of mast Q will be labeled as Q. The radius of mast P is 20 km, and the radius of mast Q is 15 km. Since the masts are 30 km apart, we'll draw mast P at a distance of 15 km to the left of mast Q. We'll use a scale of 1 cm = 5 km for this drawing.
b. We'll label the points where the two circles meet as L and M. Then, we'll draw lines PL, LQ, QM, and MP.
c. The quadrilateral PLQM is called a kite.
d. We'll shade in the locus of points that is covered by both masts.
Here's a textual representation of the drawing:
css
Copy code
P
L ___________|___________ M
/ \
/ \
20 km / 30 km \ 15 km
/ \
/ \
/ \
/ \
/_______________________________________\
Q Q
In this representation:
P and Q are the centers of the circles representing the coverage areas of the masts.
The circles around P and Q represent the coverage areas of the two masts.
L and M are the points where the circles intersect.
PL, LQ, QM, and MP are the lines connecting the respective points.
The shaded area represents the locus of points covered by both masts.
Step-by-step explanation:
