Find the coordinates if the midpoint of a line segment with endpoints (-3,4) and (7,9).

Mathematics

2 answers:

svetoff [14.1K]3 years ago

5 0

Using the midpoint formula
$\frac{ x_{1}+ x_{2} }{2}, 
 \frac{ y_{1}+ y_{2} }{2}$
$\frac{-3+7}{2},
 \frac{4+9}{2}$
$\frac{4}{2},
 \frac{13}{2}$
$(2,6.5)$
So, your answer would be (2,6.5).

Neporo4naja [7]3 years ago

5 0

Answer:

(2, $\frac{13}{2}$ ) or in simplified form (2, $6\frac{1}{2}$ ) or in decimal form (2, 6.5)

Step-by-step explanation:

Look at the image down below!! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

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The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$