Question

1. n is the midpoint of gh. the coordinates of g are (4, 3) and the coordinates of n are (5, 6). find the coordinates of h.

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 $G=(x_G,y_G)=(4,3)$ and $N=(x_N,y_N)=(5,6)$ and the coordinates of $H=(x_H,y_H)$. Then $x_N=\frac{x_G + x_H}{2}$ and $y_N=\frac{y_G + y_H}{2}$.

Step2: Solve for $x_H$

We know that $x_N=\frac{x_G + x_H}{2}$, substituting $x_G = 4$ and $x_N=5$ into the formula:
\[5=\frac{4 + x_H}{2}\]
\[10=4 + x_H\]
\[x_H=10 - 4=6\]

Step3: Solve for $y_H$

We know that $y_N=\frac{y_G + y_H}{2}$, substituting $y_G = 3$ and $y_N = 6$ into the formula:
\[6=\frac{3 + y_H}{2}\]
\[12=3 + y_H\]
\[y_H=12 - 3 = 9\]

Answer:

$(6,9)$