Question

The points (-2, -3) and (5, 2) are the end points of the diameter of a circle. Find the length of the radius of the circle.

Answer 1

Answer:

The length of the radius of the circle is 4.3 unit

Step-by-step explanation:

Given as :

The end points of the diameter of a circle = (-2, -3) and (5, 2)

Let The point A = (-2, -3)

And The point B = (5, 2)

Now The measure of the diameter of the circle = The distance between points A and B

Or, Distance = Diameter = $\sqrt{(y_2-y_1)^{2} + (x_2-x_1)^{2} }$

Or,  Diameter = $\sqrt{(2-(-3))^{2} + (5-(-2))^{2} }$

Or,  Diameter = $\sqrt{(5)^{2} + (7)^{2} }$

Or,  Diameter = $\sqrt{74}$

∴    Diameter = 8.6 unit

So, The diameter of circle = 8.6 unit

Now, The radius of circle = $\dfrac{\textrm Diameter}{2}$

Or, radius = $\dfrac{\textrm 8.6}{2}$

∴ Radius = 4.3 unit

Hence The length of the radius of the circle is 4.3 unit Answer

Answer 2

Answer:

The  length of the radius of the circle  = 4.30 units

Step-by-step explanation:

Here, the endpoints of the diameter are given as A(-2,-3) and B(5,2).

Now, the given diameter is the segment AB.

DISTANCE FORMULA

It states that for two points P(a,b) and Q(c,d), the length of segment PQ is given as  $PQ = \sqrt{(a-c)^2 + (d-b)^2}$

So, applying the formula here,

$AB = \sqrt{(5-(-2))^2 + (2-(-3))^2} = \sqrt{(5+2)^2 + (2+3)^2}\\ = \sqrt{(7)^2 + (5)^2} = \sqrt{49 + 25 } = \sqrt{74} = 8.60$

or, AB  = 8.60 Units

So, the diameter of the circle = 8.6 units

Now, Diameter = 2 x Radius

So, R = D / 2  

           = 8.6 / 2 = 4. 3

or, Radius  = 4.3 units

Hence, the  length of the radius of the circle  = 4.30 units