Question

Learning Task 3 (page 29)
A Find the distance between the two given points. Show your complete solution
1. S(-1, 6) and T(-1, 14)
4. U(-5, 2) and P(-5, 7)
2. H(-9, 3) and G(6.3)
5. AC-3, 2) and M(9.7)
3. M(0,0) and N(4,6)​

Answer 1

Given:

1. S(-1,6) and T(-1,14)

2. H(-9,3) and G(6,3)

3. M(0,0) and N(4,6)​

4. U(-5,2) and P(-5,7)

5. AC(-3, 2) and M(9,7)

To find:

The distance between the two given points.

Solution:

$Distance = \sqrt{(x_2 - x_1)^{2} + (y_2-y_1)^{2} }$

1. S(-1,6) and T(-1,14)

$d = \sqrt{(-1-(-1))^{2} + (14-6)^{2} } \\\\d = \sqrt{0^{2} + 8^{2} } \\\\d = \sqrt{8^{2} } \\\\d = 8$

Distance = 8

2. H(-9,3) and G(6,3)

$d = \sqrt{(6-(-9))^{2} + (3-3)^{2} } \\\\d = \sqrt{15^{2} + 0^{2} } \\\\d = \sqrt{15^{2} } \\\\d = 15$

Distance = 15

3. M(0,0) and N(4,6)​

$d = \sqrt{(4-0)^{2} + (6-0)^{2} } \\\\d = \sqrt{4^{2} + 6^{2} } \\\\d = \sqrt{16+36 } \\\\d = \sqrt{52} \\\\d = 2\sqrt{13} \\\\d = 7.2111$

Distance = √52 = 2√13 = 7.2111

4. U(-5,2) and P(-5,7)

$d = \sqrt{(-5-(-5))^{2} + (7-2)^{2} } \\\\d = \sqrt{0^{2} + 5^{2} } \\\\d = \sqrt{5^{2} } \\\\d = 5$

Distance = 5

5. AC(-3, 2) and M(9,7)

$d = \sqrt{(9-(-3))^{2} + (7-2)^{2} } \\\\d = \sqrt{12^{2} + 5^{2} } \\\\d = \sqrt{144+25 } \\\\d = \sqrt{169} \\\\d = 13$

Distance = 13