Question

question 1 - 25
use a coordinate plane. the position of two friends can be denoted by the points ( a(1,8) ) and ( b(7,8) ). their teacher is standing at point ( o ). the teachers distance from point ( a ) is half the distance from point ( b ). what are the coordinates of point ( o )?
( \bigcircleft(\frac{8}{3}, \frac{8}{3}
ight) )
( \bigcirc(3,4) )
( \bigcircleft(4, \frac{8}{2}
ight) )
( \bigcirc(6,5) )

Explanation:

Step1: Use the mid - point formula

The mid - point formula for 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 \(x_1=1,y_1 = 8,x_2=7,y_2 = 8\).

Step2: Calculate the \(x\) - coordinate of the mid - point

\(x=\frac{1 + 7}{2}=\frac{8}{2}=4\).

Step3: Calculate the \(y\) - coordinate of the mid - point

\(y=\frac{8+8}{2}=\frac{16}{2}=8\).

Answer:

\((4,8)\)