Question

the formula for the mid - point between two points $(x_1,y_1),(x_2,y_2)$ is $(\frac{(x_1 + x_2)}{2},\frac{(y_1 + y_2)}{2})$. points p and q on the coordinate grid below represent the locations of two observers for a science project. if the two observers both want to be the same distance from the science project, and as close as possible to it, what point best represents the location for them to put the science project? a. (6.5,6) b. (-1.5,2) c. (6,6.5) d. (2,-1.5)

Explanation:

Step1: Identify the coordinates of points P and Q

From the graph, point P has coordinates $(5,8)$ and point Q has coordinates $(8,4)$.

Step2: Apply the mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1 = 5$, $y_1=8$, $x_2 = 8$, $y_2 = 4$.
For the x - coordinate of the mid - point: $\frac{5 + 8}{2}=\frac{13}{2}=6.5$.
For the y - coordinate of the mid - point: $\frac{8 + 4}{2}=\frac{12}{2}=6$.

Answer:

A. $(6.5,6)$