Question

1) If the end points of a diameter of a circle are A (-2, 3) and B (4, -5) then the co-ordinates of its center are

a. (2, -2) b. (1, -1) c. (-1, 1) d. (-2, 2)​

Answer 1

Step-by-step explanation:

Since the two given points, (2,3) and (4,9), form a line segment, you can figure out:

1) The length of the segment (diameter of the circle), and

2) The midpoint of the segment (the center of the circle).

Let's start with the length of the segment:

Using the Pythagorean theorem,

$( {a}^{2} + {b}^{2} = {c}^{2} )</p><p>$

we can take the Δx as our a value and Δy as our b value. The length of the segment will be c.

Δx=x2−x1

Δx=4−2

Δx=2

a=2

Δy=y2−y1

Δy=9−3

Δy=6

b=6

If we plug these in, we get:

22+62=c2

4+36=c2

40=c2

2√10=c

We have our diameter of the circle now, but we want the radius so we can write the equation of the circle later:

2r=d

r=d2

r=2√102

r=√10

We'll use this later.

Now, for the midpoint, which is much simpler:

We're going to find the middle of this line, and the center's coordinate pair will be: (x1+x2/2,y1+y2/2)

This means finding the average between the xvalues of each point and the