Question

2.1. What is the distance between points R(0,3) and F(1,4)?
A. 6
B. 2
C. 8
D. 4​

Answer 1

Given Point

$\to \rm \:R (0,3) \: and \: F(1,4)$

To Find Distance Between RF

To Find Distance Between RF Formula

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

By Comparing with

$\to\rm \: R(x_1,y_1) \: and \:F (x_2,y_2)$

We get

$\rm \to \: x_1 = 0,y_1 = 3,x_2 = 1 \: and \: y_2 = 4$

Put the value on formula

$\to \rm \: RF \: = \sqrt{(1 - 0)^{2} + (4- 3)^{2} }$

$\to \rm \: RF \: = \sqrt{(1 )^{2} + (1)^{2} }$

$\to \rm \: RF \: = \sqrt{1 + 1 }$

$\to \rm \: RF \: = \sqrt{2}$

Answer

$\to \rm \: RF \: = \sqrt{2} \: units$

Answer 2

Given :-

R(0,3)

F(1,4)

To Find :-

Distance between them

Solution :-

We have

$\sf \begin{cases}\sf x_1 = 0 \\ \sf x_2 = 1\\ \sf y_1 = 3\\ \sf y_2 = 4\end{cases}$

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

$\sf Distance = \sqrt{(1-0)^2 + (4-3)^2}$

$\sf Distance = \sqrt{(1)^2 - (4-3)^2}$

$\sf Distance = \sqrt{1^2 + 1^2}$

$\sf Distance =\sqrt{1+1}$

$\sf Distance = \sqrt{2}$