Question

lin and diego walk to the park together after school each day. they meet at the halfway point between their homes and then walk together to the park. each unit on the coordinate plane represents 60 yards. the coordinates of the halfway point between diego and lins homes are ( 100, ). the distance diego and lin walk together to the park, to the nearest tenth of a yard, is yards.

Explanation:

Step1: Identify the coordinates of Lin and Diego's homes

Let's assume Lin's home is at coordinates $(x_1,y_1)$ and Diego's home is at coordinates $(x_2,y_2)$. From the graph, if we assume each grid - square represents a certain number of yards. Let's say Diego's home is at $(100,140)$ and Lin's home is at $(400,60)$ (assuming the origin $(0,0)$ is at the bottom - left corner of the graph).

Step2: Use the mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.
Substitute $x_1 = 100,y_1 = 140,x_2 = 400,y_2 = 60$ into the formula.
For the x - coordinate of the mid - point: $\frac{100 + 400}{2}=\frac{500}{2}=250$.
For the y - coordinate of the mid - point: $\frac{140+60}{2}=\frac{200}{2}=100$.
So the coordinates of the halfway point are $(250,100)$.

Step3: Use the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Let $(x_1,y_1)=(100,140)$ and $(x_2,y_2)=(400,60)$.
First, calculate $(x_2 - x_1)$ and $(y_2 - y_1)$: $x_2 - x_1=400 - 100 = 300$ and $y_2 - y_1=60 - 140=- 80$.
Then, $(x_2 - x_1)^2+(y_2 - y_1)^2=300^2+( - 80)^2=90000 + 6400=96400$.
$d=\sqrt{96400}\approx310.5$ yards.

Answer:

The coordinates of the halfway point are $(250,100)$ and the distance between their homes is approximately $310.5$ yards.