Question

The point midway between is .So the point midway between$\left(1,2\right)\text{and}\left(7,10\right)$ is .

Short answer

$\left(4,6\right)$The point midway between$\left(a,b\right)\text{and}\left(c,d\right)$ is $\left(\frac{a+c}{2},\frac{b+d}{2}\right)$. So the point midway between$\left(1,2\right)\text{and}\left(7,10\right)$ is .

Step-by-step solution

Step 1. Apply the concept of the midpoint formula.

The midpoint of the segment that joins two points$A=\left(x_1,y_1\right)\text{and}B=\left(x_2,y_2\right)$ in the Cartesian plane is denoted by $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 2. Compute the midpoint of the points. 

Consider the provided points $\left(a,b\right)\text{and}\left(c,d\right)$.

Evaluate the midpoint of the points.

Let $\left(x_1,y_1\right)=\left(a,b\right)\text{and}\left(x_2,y_2\right)=\left(c,d\right)$.

$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

Therefore, the point midway between$\left(a,b\right)\text{and}\left(c,d\right)$ is $\left(\frac{a+c}{2},\frac{b+d}{2}\right)$.

Step 3. Compute the midpoint of the points. 

$\left(1,2\right)\text{and}\left(7,10\right)$Consider the provided points $\left(1,2\right)\text{and}\left(7,10\right)$.

Evaluate the midpoint of the points.

Let $\left(a,b\right)=\left(1,2\right)\text{and}\left(c,d\right)=\left(7,10\right)$.

$\begin{array}{c}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{a+c}{2},\frac{b+d}{2}\right)\\ =\left(\frac{1+7}{2},\frac{2+10}{2}\right)\\ =\left(\frac{8}{2},\frac{12}{2}\right)\\ =\left(4,6\right)\end{array}$

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