Basic Math Examples

end points of diameter of a circle are $(- 7, 3)$ and $(5, 1)$ what is the center of the circle?

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(5 - (- 7))}^{2} + {(1 - 3)}^{2}}$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $- 7$ .

$\sqrt{{(5 + 7)}^{2} + {(1 - 3)}^{2}}$

Step 3.2

Add $5$ and $7$ .

$\sqrt{12^{2} + {(1 - 3)}^{2}}$

Step 3.3

Raise $12$ to the power of $2$ .

$\sqrt{144 + {(1 - 3)}^{2}}$

Step 3.4

Subtract $3$ from $1$ .

$\sqrt{144 + {(- 2)}^{2}}$

Step 3.5

Raise $- 2$ to the power of $2$ .

$\sqrt{144 + 4}$

Step 3.6

Add $144$ and $4$ .

$\sqrt{148}$

Step 3.7

Rewrite $148$ as $2^{2} \cdot 37$ .

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Step 3.7.1

Factor $4$ out of $148$ .

$\sqrt{4 (37)}$

Step 3.7.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 37}$

Step 3.8

Pull terms out from under the radical.

$2 \sqrt{37}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{37}$

Decimal Form:

$12.16552506 \dots$

Step 5