The end points of the diameter of a circle are P(-7,-4)and Q(-1,10).Find the coordinates of the center of this circle.
Use the midpoint formula
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To find the coordinates of the center of the circle, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using this formula, we can find the midpoint of the diameter of the circle, which will also be the center of the circle.
Given that the endpoints of the diameter are P(-7, -4) and Q(-1, 10), let's calculate the midpoint:
Midpoint = ((-7 - 1) / 2, (-4 + 10) / 2)
= (-8 / 2, 6 / 2)
= (-4, 3)
Therefore, the coordinates of the center of the circle are (-4, 3).
To find the coordinates of the center of a circle given the endpoints of its diameter, you can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Let's calculate the x-coordinate of the center:
x-coordinate of center = (x-coordinate of P + x-coordinate of Q) / 2
= (-7 + (-1)) / 2
= (-8) / 2
= -4
Now let's calculate the y-coordinate of the center:
y-coordinate of center = (y-coordinate of P + y-coordinate of Q) / 2
= (-4 + 10) / 2
= 6 / 2
= 3
Therefore, the coordinates of the center of the circle are (-4, 3).