Representing Distances

Scale is the ratio between the distance in the map and the distance in a real ground. It shows how many times the map has been reduced from the real size of the area it represents. This note contains the description on finding distances in the map.

Summary

Scale is the ratio between the distance in the map and the distance in a real ground. It shows how many times the map has been reduced from the real size of the area it represents. This note contains the description on finding distances in the map.

Things to Remember

  • 1 cm represents 1 m i.e. 1 cm = 1 m
  • Scale in the ratio between the distance in the map and the distance in real ground. 
  • To find the shortest distance between two places or along a straight road, measure carefully with a ruler, then change the cms to the real measurement.

MCQs

No MCQs found.

Subjective Questions

Q1:

Find a and b if (4a, 6b) = (8, 12)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(4a, 6b) = (8, 12)<br>Comparing the corresponding first and second components,<br>or, 4a = 8<br>or, a = \(\frac{8}{4}\)<br>or, a = 2<br>And,<br>or,6b = 12<br>or, b = \(\frac{12}{6}\)<br>or, b = 2<br>&there4; a = 2 and b = 2.</p>

Q2:

Find m and n if (5m+1, −10) = (16, 3n+2)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(5m+1,&minus;10) = (16, 3n+2)<br>Comparing the corresponding first and second cpmponents,<br>or, 5m + 1 = 16<br>or, 5m = 16 &minus; 1<br>or, 5m = 15<br>or, m = \(\frac{15}{5}\)<br>or, m = 3<br>And,<br>or, 3n + 2 = &minus;10<br>or, 3n = &minus;10 &minus; 2<br>or, 3n = &minus;12<br>or, n = \(\frac{&minus;12}{3}\)<br>or, n = &minus;4<br>&there4; m = 3 and n = &minus;4.</p>

Q3:

Find the value of x and y if (2x, 3y) = (−6, 9)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Comparing the coressponding first and second components,<br>Here,<br>(2x, 3y) = (&minus;6, 9)<br>or, 2x = &minus;6<br>or, x = \(\frac{&minus;6}{2}\)<br>or, x = &minus;3<br>And,<br>or, 3y = 9<br>or, y = \(\frac{9}{3}\)<br>or, y = 3<br>&there4; x = &minus;3 and y = 3.</p>

Q4:

Find the value of i and j if (n − 2, \(\frac{m}{4}\)) = (2, 0)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(n&minus; 2, \(\frac{m}{4}\)) = (2, 0)<br>Comparing the corresponding first and second components,<br>or, n &minus; 2 = 2<br>or, n = 2 + 2<br>or, n = 4<br>And,<br>or,\(\frac{m}{4}\) = 0<br>or, m = 0<br>&there4; n = 4 and m = 0</p>

Q5:

Find the value of a and b if (35, −5) = (a − 2, b + 3)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(35, &minus;5) = (a &minus; 2, b + 3)<br>Comparing the corresponding value First and second components,<br>or, a &minus; 2 = 35<br>or, a = 35 + 2<br>or, a = 37<br>And,<br>or, b + 3 = &minus;5<br>or, b = &minus;5 &minus; 3<br>or, b = &minus;8<br>&there4; a = 37 and b = &minus;8</p>

Q6:

Find the value of m and n if (\(\frac{m}{2}\), 3) = (3, \(\frac{n}{2}\) + 1)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(\(\frac{m}{2}\), 3) = (3, \(\frac{n}{2}\) + 1)<br>Comparing the corresponding first and second components,<br>or, \(\frac{m}{2}\) = 3<br>or, m = 3 &times; 2<br>or, m = 6<br>And,<br>or, \(\frac{n}{2}\) + 1 = 3<br>or, \(\frac{n}{2}\) = 3 &minus; 1<br>or, \(\frac{n}{2}\) = 2<br>or, n = 2 &times; 2<br>or, n = 4<br>&there4; m = 6 and n = 4</p>

Q7:

Find the value of x and y if (−x, 3) = ( 4, −y)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(&minus;x, 3) = ( 4, &minus;y)<br>Comparing the corresponding first and second components,<br>or, &minus;x = 4<br>or, x = &minus;4<br>And,<br>or, &minus;y = 3<br>or, y = &minus;3<br>&there4; x = &minus;4 and y = &minus;3</p>

Q8:

Find the value of x and y if (5x, 7y) = (15, 28)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(5x, 7y) = (15, 28)<br>Comparing thr corresponding first and second components,<br>or, 5x = 15<br>or, x = \(\frac{15}{5}\)<br>or, x = 3<br>And,<br>or, 7y = 28<br>or, y = \(\frac{28}{7}\)<br>or, y = 4<br>&there4; x = 3 and y = 4</p> <p></p>

Q9:

Find the value of if (a − 2, b + 1) = (4, 2b)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(a &minus; 2, b + 1) = (4, 2b)<br>Comparing the corresponding first and second components,<br>or,a &minus; 2 = 4<br>or, a = 4 + 2<br>or, a = 6<br>And,<br>or, b + 1 = 2b<br>or, 2b &minus; b = 1<br>or, b = 1<br>&there4; a = 6 and b = 1</p>

Q10:

Find the value of p and q if (p + 4, 6) = (10, q)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(p + 4, 6) = (10, q)<br>Comparing the corresponding first and second components,<br>or, p + 4 = 10<br>or, p = 10 &minus; 4<br>or, p = 6<br>And,<br>or, q = 6<br>&there4; p = 6 and q = 6</p>

Q11:

Find the value of a and b (a + 3, b) = (10, 5)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(a + 3, b) = (10, 5)<br>Comparing the corresponding first and second components,<br>or, a + 3 = 10<br>or, a = 10 &minus; 3<br>or, a = 7<br>And,<br>or, b = 5<br>&there4; a = 7 and b = 5</p>

Q12:

Find the value of x and y if (6, −y) = (−x, −4)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(6,&minus;y) = (&minus;x,&minus;4)<br>Comparing the corresponding first and second components,<br>or, &minus;x = 6<br>or, x = &minus;6<br>And,<br>or, &minus;y = &minus;4<br>or, y = 4<br>&there4; x = &minus;6 and y = 4</p>

Q13:

Find the value of a and b if (a, 3) = (4, b + 1)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br>(a, 3) = (4, b + 1)<br>Comparing the corresponding first and second components,<br>or, a = 4<br>And,<br>or, b + 1 = 3<br>or, b = 3 &minus; 1<br>or, b = 2<br>&there4; a = 4 and b = 2</p>

Q14:

Find the value of x and y if (x, y − 2) = (6, 8)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:;</p> <p>Here,<br>(x, y &minus; 2) = (6, 8)<br>Comparing the corresponding first and second components,<br>or, x = 6<br>And,<br>or, b &minus; 2 = 8<br>or, b = 8 + 2<br>or, b = 10<br>&there4; x = 6 and b = 10</p>

Q15:

Find the value of p and q if (−p, 6q) = (3, 36)


Type: Short Difficulty: Easy

Show/Hide Answer
Answer: <p>Solution:</p> <p>Here,<br> (&minus;p, 6q) = (3, 36)<br>Comparing the corresponding first and second components,<br>or,&minus;p = 3<br>or, p = &minus;3<br>And,<br>or, 6q = 36<br>or, q = \(\frac{36}{6}\)<br>or, q = 6<br>&there4; p = &minus;3 and q = 6</p>

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Representing Distances

Representing Distances

Scale-drawing

This table in 2 m long and 1 m wide. A life-size plan would not fit on a page so it must be drawn to scale so that the shape stays correct and so that anyone looking at the plan can easily find true sizes. each meter of the table can be shown by 1 cm on the plan. check that the plan incorrect. the scale can be given in 4 ways:

  1. 1 cm represents 1 m i.e. 1 cm = 1 m
  2. as a ratio 1:100
    (1 cm on the map is 1 m = 100 cm of real object.)
  3. as a fraction, 1 the map in 100 times smaller than the table.
    100
    (1:100 in a very large scale, suitable for plans of rooms.)
  4. with a line 0 to 1 m

The scale is the ratio between the distance on the map and the distance on a real ground. It shows how many times the map has been reduced from the real size of the area it represents.

Measuring distances

To find the shortest distance between two places or along a straight road, measure carefully with a ruler, then change the cm to the real measurement

For example, the distance between the zoo and Pulchowk stupa in 1.3 cm and the scale in 1:50,000
1.3 * 50,000 = 65,000
so the real distance in 65,000 cm = 650 m

Lesson

Our Earth

Subject

Social Studies and Population Education

Grade

Grade 8

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