Question

At 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text, the temperature is halfway between the temperature at 2 \text{ p.m.}2 p.m.2, start a text, space, p, point, m, point, end text and the temperature at 8 \text{ p.m.}8 p.m.8, start a text, space, p, point, m, point, end text

What coordinates represent the temperature at 5 \text{ p.m.}5 p.m.5, start a text, space, p, point, m, point, end text?

Answer 1

(5,2)

Explanation:

From the graph attached below:

• The coordinate for the temperature (in degree Celsius) at 2 p.m. is (2,7)
• The coordinate for the temperature (in degree Celsius) at 8 p.m. is (8,-3)

Since the temperature at 5 p.m. is halfway between the temperature at 2 p.m. and 8 p.m. , the coordinate of the temperature at 5 p.m. is the midpoint of (2,7) and (8,-3).

For two coordinate points
`A(x_1,y_1)$ and B(x_2,y_2)`

`\text{Midpoint of AB }=(1)/(2) \left( x_1+x_2,y_1+y_2 \right)`

Therefore, the coordinates for 5p.m.

`=(1)/(2) \left( 2+8,7+(-3) \right) \\=(1)/(2) \left( 10,4 \right)\\\\=(5,2)`