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umka21 [38]
4 years ago
8

WILL GIVE BRAINLIEST ANSWER TO WHOEVER ANSWERS FIRST

Mathematics
1 answer:
xz_007 [3.2K]4 years ago
5 0

These are easy, we just have to average the corresponding coordinates.

First we do a few one dimension ones, the midpoint of points on a number line:

1. 9 & 6

\dfrac{9 + 6}{2} = \dfrac{15}{2}

2. -2 & 7

\dfrac{-2 + 7}{2} = \dfrac{5}{2}

3. -3 & -13

\dfrac{-3 + -13}{2} = -8

For the rest of these we're in 2D, the Cartesian plane.

4. (0,0), (9,3)

\left( \dfrac{0+9}{2}, \dfrac{0+3}{2} \right) = ( \frac 9 2, \frac 3 2)

5. (-2,1), (3,6)

\left( \dfrac{-2+3}{2}, \dfrac{1+6}{2} \right) = ( \frac 1 2, \frac 7 2)

6. (-3, 14), (10, -4)

\left( \dfrac{-3+10}{2}, \dfrac{14+-4}{2} \right) = ( \frac 7 2, 5)

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Option A: (x+3)^2+(y+2)^2=4 is the equation of the circle

Explanation:

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Let us subtract 10 from both sides of the equation.

Thus, we have,

x^{2} +y^2+6x+4y=-9

Grouping the terms,we have,

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(x^{2} +6x+9-9)+(y^2+4y)=-9

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(x^{2} +6x+9)+(y^2+4y)=-9+9

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Thus, we have,

(x+3)^2+(y^2+4y+4-4)=0

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(x+3)^2+(y^2+4y+4)=4

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Thus, the equation of the circle in standard form is (x+3)^2+(y+2)^2=4

Hence, Option A is the correct answer.

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4 years ago
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