All categories

3 years ago

The endpoints of a diameter of a circle are A(2,1) and B(5,5). Find the area of the circle in terms of pi.

Mathematics

1 answer:

Tcecarenko [31]3 years ago

4 0

Answer:

The area of the circle is $A=6.25\pi\ units^{2}$

Step-by-step explanation:

step 1

Find the diameter of circle

we know that

The diameter of the circle is equal to the distance AB

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$AB=\sqrt{(5-1)^{2}+(5-2)^{2}}$

$AB=\sqrt{(4)^{2}+(3)^{2}}$

$AB=\sqrt{25}$

$AB=5\ units$

therefore

the diameter of the circle is

$D=5\ units$

step 2

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

$r=5/2=2.5\ units$ ----> the radius is half the diameter

substitute

$A=\pi (2.5)^{2}$

$A=6.25\pi\ units^{2}$

You might be interested in

How many quarter pound 1/4 packets can a garden shop make out of 8 pounds of the plant food

Step2247 [10]

32

Sorry, I couldn't really think of a way to explain but the best I can is by multiplying the 4 by 8 to get the answer of 32

8 0

3 years ago

Read 2 more answers

Which group contains triangles that are all similar?

torisob [31]

Answer:

Triangles represented by option B are similar triangles.

Step-by-step explanation:

Please find the attachment.

We have been given 4 group of triangles and we are asked to find which group contains similar triangles.

A. We can see from our diagram that triangles provided in option A are not similar.

The first triangle is an isosceles right triangle as it has 2 angles each having measure 45 degrees. By angle sum property the measure of 3rd angle will be:

$180^o-(45^o+45^o)=180^o-90^o=90^o$

The second triangle is an equilateral triangle as all the sides equal to 7 units, so all angles will be equal to 60 degrees.

The 3rd triangle is an isosceles triangle as it has 2 angles each having measure 53 degrees. By angle sum property the measure of 3rd angle will be:

$180^o-(53^o+53^o)=180^o-106^o=74^o$

We can see that none of the triangles have same angle measures, therefore, option A is not a correct choice.

B. The triangles provided in option B are similar triangles as each triangle have one right angle and they are sharing the same vertex.

Let us assume that the common vertex has x degrees angle, then by angle sum property the measure of 3rd angle in each triangle will be $180-90-x=90-x$ degrees. Therefore, the triangles provided in option B are similar triangles by AAA similarity theorem.

C. The triangles provided in option C are not similar triangles as we are not told that the given lines are parallel or not. In addition the bottom figure is a quadrilateral as it has 4 angles, Therefore, the given triangles are not similar triangles.

D. We can see that our given triangles have vertical angles, so their measure will be 32 degrees. Since the given side lengths are different, therefore, this group of triangles is not similar.