Question

find the distance between the point (2,-2) and (4,5)

Answer 1

Answer:

the distance between (2,-2) point is |2-(-2)|=|2+2|=|4|=4

the distance between (4,5) point is |4-5|=|-1|=1

Answer 2

ANSWER:  

The distance between two points (2,-2) and (4,5)  is $\sqrt{53} \text { units. }$

SOLUTION:

Given, two points are (2, -2) and (4, 5).

We need to find the distance between above two points.

We know that, distance between two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is given by:

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

$\text { here, } x_{1}=2, y_{1}=-2, x_{2}=4 \text { and } y_{2}=5$

$\text { Now, distance }=\sqrt{(4-2)^{2}+(5-(-2))^{2}}$

$\begin{array}{l}{\text { Distance }=\sqrt{(4-2)^{2}+(5+2)^{2}}} \\ {=\sqrt{(2)^{2}+(7)^{2}}} \\ {=\sqrt{4+49}=\sqrt{53}}\end{array}$

Hence the distance between two points (2,-2) and (4,5)  is $\sqrt{53} \text { units. }$