Question

Johnny Awesome lives at coordinates (-6, -4). His friend Jack Black lives at (4, 8)If they wanted to meet exactly halfway between their houses, at what coordinate would they meet? (Hint, you may want to use some graph paper to plot the points.)

Answer 1

SOLUTION:

Step 1:

In this question, we are given that:

Johnny Awesome lives at coordinates (-6, -4).

His friend Jack Black lives at (4, 8)

If they wanted to meet exactly halfway between their houses,

At what coordinate would they meet?

Step 2:

Comparing the two points:

( -6, - 4 ) and ( 4, 8 )

The mid-point of the two points can be calculated thus:

$(\bar{x},\bar{y})\text{ = ( }\frac{x_1+_{}x_2}{2}\text{ , }\frac{y_1+y_2}{2})$$\begin{gathered} (\bar{x},\bar{y})\text{ = ( }\frac{-6+4}{2}\text{ , }\frac{-4+8}{2})_{} \\ (\bar{x},\bar{y})\text{ = (}\frac{-2}{2},\text{ }\frac{4}{2}) \\ (\bar{x},\bar{y})\text{ = ( }-1,\text{ 2 )} \end{gathered}$

Step 3:

The graph showing the points are as follows:

CONCLUSION:

The co-ordinates exactly halfway between their houses =

$(-\text{ 1, 2 )}$