Question

1. find the mid - point and distance given the two endpoints (12,15) and (-8, - 2)
2. (-3,5) and (14,28)

15.

Explanation:

for 13: Midpoint and Distance of (12,15) and (-8,-22)

Step1: Calculate midpoint x

$\frac{12 + (-8)}{2} = 2$

Step2: Calculate midpoint y

$\frac{15 + (-22)}{2} = -3.5$

Step3: Calculate distance

$\sqrt{(-8 - 12)^2 + (-22 - 15)^2} = \sqrt{(-20)^2 + (-37)^2} = \sqrt{1769}$

for 14: Midpoint and Distance of (-3,5) and (14,28)

Step1: Calculate midpoint x

$\frac{-3 + 14}{2} = 5.5$

Step2: Calculate midpoint y

$\frac{5 + 28}{2} = 16.5$

Step3: Calculate distance

$\sqrt{(14 - (-3))^2 + (28 - 5)^2} = \sqrt{17^2 + 23^2} = \sqrt{818}$

for 15: Midpoint and Distance (assuming A(-6,9), B(6,-3))

Step1: Calculate midpoint x

$\frac{-6 + 6}{2} = 0$

Step2: Calculate midpoint y

$\frac{9 + (-3)}{2} = 3$

Step3: Calculate distance

$\sqrt{(6 - (-6))^2 + (-3 - 9)^2} = \sqrt{12^2 + (-12)^2} = 12\sqrt{2}$

Answer:

1. Midpoint: (2, -3.5), Distance: $\sqrt{1769}$
2. Midpoint: (5.5, 16.5), Distance: $\sqrt{818}$
3. Midpoint: (0, 3), Distance: $12\sqrt{2}$