Triangle DEF has vertices located at D (2, 1), E (3, 5), and F (6, 2). Part A: Find the length of each side of the triangle. Show your work. (4 points) Part B: Find the slope of each side of the triangle. Show your work. (3 points) Part C: Classify the triangle. Explain your reasoning. (3 points)

DE = units, Slope = 4

EF=  units, Slope = -1

DF = units, Slope =

Isosceles acute angled triangle.

Step-by-step explanation:

Given three points:

D (2, 1),

E (3, 5), and

F (6, 2)

To find:

a) Length of each side.

b) Slope of each side.

c) Classification of triangle.

Solution:

Please refer to the attached image for the triangle.

Length can be calculated by using Distance formula:

Formula for slope is given as:

For DE:

For EF:

For DF:

We can see that DE = DF

So, the triangle is Isosceles acute angled.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: