Question

7 - 9: given coordinates r(-6, -2), s(7, 2), and t(0, 6), use the graph and the correct formulas to find each.
distance formula: $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
midpoint formula: $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$

1. __________ find rt.
2. __________ find rs.
3. __________ find the midpoint of $overline{rt}$.

Explanation:

Step1: Identify coordinates for RT

For points R(-6,-2) and T(0,6), let $(x_1,y_1)=(-6,-2)$ and $(x_2,y_2)=(0,6)$.

Step2: Apply distance formula for RT

$RT=\sqrt{(0 - (-6))^{2}+(6 - (-2))^{2}}=\sqrt{(6)^{2}+(8)^{2}}=\sqrt{36 + 64}=\sqrt{100}=10$

Step3: Identify coordinates for RS

For points R(-6,-2) and S(7,2), let $(x_1,y_1)=(-6,-2)$ and $(x_2,y_2)=(7,2)$.

Step4: Apply distance formula for RS

$RS=\sqrt{(7-(-6))^{2}+(2 - (-2))^{2}}=\sqrt{(13)^{2}+(4)^{2}}=\sqrt{169+16}=\sqrt{185}$

Step5: Identify coordinates for mid - point of RT

For points R(-6,-2) and T(0,6), let $(x_1,y_1)=(-6,-2)$ and $(x_2,y_2)=(0,6)$.

Step6: Apply mid - point formula for RT

Mid - point of RT = $(\frac{-6 + 0}{2},\frac{-2+6}{2})=(-3,2)$

Answer:

1. 10
2. $\sqrt{185}$
3. (-3,2)