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3 years ago

15

How do the ratios of lengths, areas, and volumes compare in similar solids?

1 answer:

kondor19780726 [428]3 years ago

7 0

If the ratio between the sides is $r$ , the ratio between the areas will be $r^2$ and the ratio between the volumes will be $r^3$

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What are the coordinates of the centroid of a triangle with vertices A(−3, 1) , B(1, 6) , and C(5, 2) ? Enter your answer in the

kirza4 [7]

<u>ANSWER</u>: The centroid is (1,3)

<u>Explanation:</u>

The centroid is the intersection of the medians of the triangle.

So we need to find the equation of any two of the medians and solve simultaneously.

Since the median is the straight line from one vertex to the midpoint of the opposite side, we find the midpoint of any two sides.

We find the midpoint of AC using the formula;

$N=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$N=(\frac{-3+5}{2}, \frac{1+2}{2})$

$N=(\frac{2}{2}, \frac{3}{2})$

$N=(1, \frac{3}{2})$

The equation of the median passes through $B(1,6)$ and $N=(1, \frac{3}{2})$ .

This line is parallel to the y-axis hence has equation

$x=1$ -------first median.

We also find the midpoint M of BC.

$M=(\frac{1+5}{2}, \frac{6+2}{2})$

$M=(\frac{6}{2}, \frac{8}{2})$

$M=(3, 4)$

The slope of the median, AM is

$Slope_{AM}=\frac{4-1}{3--3}$

$Slope_{AM}=\frac{3}{6}$

$Slope_{AM}=\frac{1}{2}$

The equation of the median AM is given by;

$y-y_1=m(x-x_1)$

We use the point M and the slope of AM.

$y-4=\frac{1}{2}(x-3)$

$2y-8=(x-3)$

$2y-x=-3+8$

$2y-x=5$ -------Second median

We now solve the equation of the two medians simultaneously by putting $x=1$ in to the equation of the second median.

$2y-1=5$

$2y=5+1$

$2y=6$

$y=3$

Hence the centroid has coordinates $(1,3)$

7 0

3 years ago

Read 2 more answers

PLEASE HELP!!! ILL GIVE BRAINLIEST<br><br><br> what is the function rule is slope

sergey [27]

Answer:

here!

Step-by-step explanation:

How to write a function rule using the concept of slope. Let us do this for example #3. The goal is use the equation y = mx + b. y = 4x + b. Use (1,6) to find b. 6 = 4 + b.

8 0

3 years ago

A braclet is $60 and additional $10 dollars for each charm what would the equation be in y=mx+b form?? HELLLLPPP!!

disa [49]

Y= 10x+60 is the answer i think

6 0

3 years ago

Please help!! I need ASAP 10 points <3

Readme [11.4K]

5m+8 that’s it I’m pretty sure

5 0

3 years ago

Four more than double a number is 100 what is the answer?

algol13

Answer:

the number would be 48 i think

Step-by-step explanation:

48 + 48 = 96

96 + 4 = 100

7 0

3 years ago