Question

fill in the blank 2 points. 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 (type your answer). the distance diego and lin walk together to the park, to the nearest tenth of a yard, is (type your answer) yards.

Explanation:

Step1: Assume coordinates of Lin and Diego's homes

Let's assume Lin's home is at point $(x_1,y_1)$ and Diego's home is at point $(x_2,y_2)$ on the coordinate - plane. First, we need to read the coordinates from the graph. Suppose Lin's home is at $(x_1,y_1)=(40,40)$ and Diego's home is at $(x_2,y_2)=(10,10)$ (assuming the grid - based coordinates on the graph, where each unit represents 60 yards).

Step2: Use the mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ in a 2D plane is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Substituting the values, we get $(\frac{40+10}{2},\frac{40 + 10}{2})=(25,25)$.

Step3: Calculate the distance from one of the points to the mid - point

We can use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let's calculate the distance from Diego's home $(10,10)$ to the mid - point $(25,25)$.
$d=\sqrt{(25 - 10)^2+(25 - 10)^2}=\sqrt{15^2+15^2}=\sqrt{225 + 225}=\sqrt{450}\approx21.21$. Since each unit represents 60 yards, the actual distance is $21.21\times60 = 1272.6$ yards.

Answer:

1272.6 yards