In , m = 90 ° . If AC = 6 and BC = 8, find the distance from vertex C to the midpoint of hypotenuse .
A)3
B)4
C)5
D)5.6

Question

In  , m  = 90 ° . If AC = 6 and BC = 8, find the distance from vertex C to the midpoint of hypotenuse  .
A)3 
B)4 
C)5 
D)5.6

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can find that AB = $\sqrt{6^2+8^2}=10$. Since we know that $\angle BAC = 90^{\circ}$, we can use the Pythagorean theorem again to find the length of the hypotenuse, which is $\sqrt{6^2+8^2+10^2}=2\sqrt{15}$.
Using the midpoint formula, we can find the midpoint of the hypotenuse to be $\left(\frac{6}{2},\frac{8}{2},\frac{2\sqrt{15}}{2}ight)=(3,4,\sqrt{15})$.
To find the distance from vertex C to the midpoint, we can use the distance formula: $\sqrt{(3-6)^2+(4-0)^2+(\sqrt{15}-0)^2}=\sqrt{9+16+15}=\sqrt{40}=2\sqrt{10} \approx \boxed{	extbf{(C) } 5}$.

In , M = 90 °