Question

question 1-11
road m is set to be constructed exactly halfway between city a and city b. city a is located at point (2, 3) and road m will be located at point (5, 4.5) on a map. what are the coordinates of city b on the map?
(2.5, 3.75)
(6, 8)
(8, 6)
(6, 8.5)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of City A be $(x_1,y_1)=(2,3)$ and the coordinates of the mid - point (Road M) be $(x_m,y_m)=(5,4.5)$, and the coordinates of City B be $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the known values: $5=\frac{2 + x_2}{2}$. Cross - multiply: $10 = 2+x_2$. Then $x_2=10 - 2=8$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the known values: $4.5=\frac{3 + y_2}{2}$. Cross - multiply: $9 = 3+y_2$. Then $y_2=9 - 3=6$.

Answer:

C. $(8,6)$