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AnnyKZ [126]
3 years ago
15

Given (10,4) and (2,8)

Mathematics
1 answer:
Mariulka [41]3 years ago
5 0
(10,4)(2,8)
slope = (8 - 4) / (2 - 10) = 4 / -8 = -1/2

y= mx + b
slope(m) = -1/2
(2,8)....x = 2 and y = 8
now we sub and find b, the y int
8 = -1/2(2) + b
8 = -1 + b
8 + 1 = b
9 = b

slope intercept form is : y = -1/2x + 9 <====

1/2x + y = 9...multiply everything by 2
x + 2y = 18 <== standard form

point slope : y - y1 = m(x - x1)...there can be 2 answers for this...
(1) using (10,4).......y - 4 = -1/2(x - 10)
(2) using (2,8)....y - 8 = -1/2(x - 2)
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Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of th
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the main formula of the circle's equation is 
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<span>Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2), so we have exactly three equation:
</span>
(0-x)² + (0-y)² = R², circle O passes through A
x²+y²= R²
(-3 -x)² + (0-y)² = R², circle O passes through B
(-3 -x)² + (y)² = R²
(1-x)² + (2-y)² = R², circle O passes through A
(1-x)² + (2-y)² = R²

and we know that R= OA = OC= OB, 
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x²+y² = (-3 -x)² + (0-y)² , it implies x² = 9+ x² + 6x , and then -9/6=x, x= -3/2
and when OA = OC
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the center is C(-3/2, 2)
7 0
4 years ago
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