Question

find the distance between the following points
1 a(4,8) and b(8,16)
2 c(-3,-7) and d(-10,4)
3 e(-12,-8) and f(10,12)

Answer 1

Answer :-

Distance between point

1. a(4,8) & b(8,16)

by using distance formula

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

= $\sqrt{ (8 - 4 )^2 + (16 - 8 )^2 }$

= $\sqrt{ (4 )^2 + (8 )^2 }$

= $\sqrt{ 16 + 64 }$

= $\sqrt{80}$

= $4\sqrt{5}$

2. c(-3 , -7 ) & d(-10, 4)

= $\sqrt{ (-10 - (-3) )^2 + (4 - (-7) )^2 }$

= $\sqrt{ (-10 + 3 )^2 + (4 + 7)^2 }$

= $\sqrt{ (-7)^2 + (11 )^2 }$

= $\sqrt{ 49 + 121}$

= $\sqrt{ 170 }$

3. e(-12 , 18) & f(10,12)

$= \sqrt{ {(10 - ( - 12))}^{2} + {(12 - ( - 8))}^{2} } \\ \\ = \sqrt{ {(10 + 12)}^{2} + {(12 + 8)}^{2} } \\ \\ = \sqrt{ {22}^{2} + {20}^{2} } \\ \\ = \sqrt{484 + 400} \\ \\ = \sqrt{884} \\ \\ = 2 \sqrt{221}$

Hope it helps