Chapter 1.8, Problem 3E

The point midway between (a, b) and (c, d) is __________. So the point midway between (1, 2) and (7, 10) is __________.

To determine

To fill: The formula of midpoint between two coordinates and the point midway between the given coordinates.

Answer to Problem 3E

Point midway between the points $\left(a,b\right)$ and $\left(c,d\right)$ is $\left\{\frac{\left(c+a\right)}{2},\frac{\left(d+b\right)}{2}\right\}$ and the point midway between the given coordinates $\left(1,2\right)$ and $\left(7,10\right)$ is $\left\{4,6\right\}$

Explanation of Solution

Formula used:

Midpoint between the line segments $A\left(x_1,y_1\right)\text{to}B\left(x_2,y_2\right)=\left\{\frac{\left(x_2+x_1\right)}{2},\frac{\left(y_2+y_1\right)}{2}\right\}$

Calculation:

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

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

Substitute a in place of $x_1$, b in place of $y_1$, c in place of $x_2$ and d in place of $y_2$.

$\left\{\frac{\left(c+a\right)}{2},\frac{\left(d+b\right)}{2}\right\}$

Point midway between the points $\left(a,b\right)$ and $\left(c,d\right)$ is $\left\{\frac{\left(c+a\right)}{2},\frac{\left(d+b\right)}{2}\right\}$

Section2:

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

Substitute 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 10 for $y_2$.

$\begin{array}{c}\text{Mid}\text{point}=\left\{\frac{\left(7+1\right)}{2},\frac{\left(10+2\right)}{2}\right\}\\ =\left\{\frac{8}{2},\frac{12}{2}\right\}\\ =\left\{4,6\right\}\end{array}$

Therefore, the point midway between the given coordinates $\left(1,2\right)$ and $\left(7,10\right)$ is $\left\{4,6\right\}$.