Chapter 1.8, Problem 2E

To determine

To fill: The formula of distance between two coordinates and the distance between the given coordinates.

Answer to Problem 2E

The coordinate of the point is $\left(3,-5\right)$ and distance between the points $\left(1,2\right)$ and $\left(7,0\right)$ is 10.

Explanation of Solution

Given:

The given coordinates are $\left(a,b\right)$ and $\left(c,d\right)$.

Formula used:

$d\left(A,B\right)=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Where, $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are coordinate of point A and B respectively.

Calculation:

Section1:

Substituting the value of given coordinates in the formula to find the distance between them.

Substitute a for $x_1$, b for $y_1$, c for $x_2$ and d for $y_2$.

$d=\sqrt{{\left(c-a\right)}^2+{\left(d-b\right)}^2}$

Therefore, distance between the points $\left(a,b\right)$ and $\left(c,d\right)$ is $\sqrt{{\left(c-a\right)}^2+{\left(d-b\right)}^2}$.

Section2:

The given coordinates are $\left(1,2\right)$ and $\left(7,10\right)$.

Substituting the value of given coordinates in the formula to find the distance between them.

Substitute 1 for $x_1$ 2 for $y_1$, 7 for $x_2$ and 0 for $y_2$.

$\begin{array}{c}d=\sqrt{{\left(7-1\right)}^2+{\left(10-2\right)}^2}\\ =\sqrt{{\left(6\right)}^2+{\left(8\right)}^2}\\ =\sqrt{36+64}\\ =10\end{array}$

Therefore, distance between the points $\left(1,2\right)$ and $\left(7,0\right)$ is 10.