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2 years ago

A circle has a diameter with endpoints A (-4,4) and B (2,-3) . Which coordinates represent the center of the circle?

Mathematics

1 answer:

Sergio [31]2 years ago

6 0

Answer:

The coordinates of the center of the circle is (-1,-0.5)

Step-by-step explanation:

The coordinates of the center are only the midpoint coordinates of the endpoint

Mathematically, that will be;

(x,y) = (x1 + x2)/2, (y1 + y2)/2

= (-4+2)/2, (4-3)/2

= (-2/2),(-1/2)

= (-1, -0.5)

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The cosine rule is given as;

$c = \sqrt{a^2 + b^2 - 2ab cos \alpha }$

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$c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}$

$c = \sqrt{533 - 308 * 0. 7660}$

$c = \sqrt{533 - 235. 93}$

$c = \sqrt{297. 072}$

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Using sine rule

$\frac{a}{sin A } = \frac{c}{sin C}$

$\frac{a}{sin 70} = \frac{17. 24}{sin 40}$

Cross multiply

$a$ × $sin 60$ = $c$ × $sin 70$

$a$ × $0. 8660$ = $17. 24$ × $0. 9397$

$a = \frac{16. 20}{0. 8660}$

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

Learn more about isosceles trapezoid here:

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