Question

Use a ruler to measure distance (in cm)
between the places represented by the dots.
If the scale used is 1 cm = 8 km, find the actual distance between:
a. point A and point B.
b. point C and point D.
c. point C and point F
d. point A and point F.
​

Answer 1

SOLUTION

GIVEN

Use a ruler to measure distance (in cm)

between the places represented by the dots.

If the scale used is 1 cm = 8 km,

TO DETERMINE

The actual distance between

a. point A and point B.

b. point C and point D.

c. point C and point F

d. point A and point F.

EVALUATION

As from figure we see that

AC = 4.5 cm , BC = 2 cm , CE = 8 cm , DE = 1 cm , EF = 3 cm

a. From the given we see that

The distance between A and B

= AB

= AC - BC

= ( 4.5 - 2 ) cm

= 2.5 cm

Now in the scale used is 1 cm = 8 km

So the actual distance between the point A and point B

= ( 2.5 × 8 ) km

= 20 km

b. From the given we see that

The distance between C and D

= CD

= CE - DE

= ( 8 - 1 ) cm

= 7 cm

Now in the scale used is 1 cm = 8 km

So the actual distance between the point C and point D

= ( 7 × 8 ) km

= 56 km

c. From the given we see that

The distance between C and F

= CF

= 8.5 cm

Now in the scale used is 1 cm = 8 km

So the actual distance between the point C and point F

= ( 8.5 × 8 ) km

= 68 km

Verification using Pythagoras theorem

CF

$= \sf{ \sqrt{ {8}^{2} + {3}^{2} } \: \: \: cm}$

$= \sf{ \sqrt{ 64 + 9} \: \: \: cm}$

$= \sf{ \sqrt{ 73 } \: \: \: cm}$

$= \sf{8.544 \: \: \: cm}$

d. We draw a line FG parallel to CE such that CE = FG = 8 cm and CG = 3 cm

∴ AG

= AC - GC

= ( 4.5 - 3) cm

= 1.5 cm

∴ The distance between A and F

= AF

= 8.1 cm

Now in the scale used is 1 cm = 8 km

So the actual distance between the point A and point F

= ( 8.1 × 8 ) km

= 64.8 km

Verification using Pythagoras theorem

AF

$= \sf{\sqrt{ {(1.5)}^{2} + {(8)}^{2}} \: \: cm }$

$= \sf{\sqrt{2.25 + 64} \: \: cm }$

$= \sf{\sqrt{66.25} \: \: cm }$

$= \sf{8.139 \: \: cm }$

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