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2 years ago

Please help It hard for me

Mathematics

1 answer:

gizmo_the_mogwai [7]2 years ago

8 0

Answer:

The wolf lives in a cave = オオカミはどうくつにすんでいます

The teacher looked at the animals = せんせいはどうぶつをみました

Step-by-step explanation:

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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]

ANSWER: The centroid is (1,3)

Explanation:

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

2 years ago

Read 2 more answers

1.3.12

kondaur [170]

Answer:

Step-by-step explanation:

The formula for calculating the midpoint of two coordinates is expressed as shown;

M(X, Y) = [(x1+x2)/2, (y1+y2)/2]

Given the midpoint of ST to be ((6, -2) and one endpoint T is (0,2), according to expression above;

X = (x1+x2)/2

Y = (y1+y2)/2

From the coordinates, X = 6, Y = -2, x1 = 0 and y1 = 2, to get x2 and y2;

X = (x1+x2)/2

6 = (0+x2)/2

cross multiply

12 = 0+x2

x2 = 12-0

x2 = 12

For 2;

Y = (y1+y2)/2

-2 = (2+y2)/2

cross multiply

-4 = 2+y2

y2 = -4-2

y2 = -6

Hence the other endpoint S(x2, y2) is (12, -6)

3 0

3 years ago

PLEASE HELP FAST 100 EASY POINTS WILL MARK BRAINLEST!!!

spin [16.1K]

Answer:

$y=-1x+8 \\or\\y=-x+8$

Step-by-step explanation:

Okay so we know that line on the triangle DEF that's parallel to the line BC is EF. This because they have the same slope and we can prove that while solving for slope-intercept form.

First we figure out our points for both the lines:

BC: $B=(-2,4) \\C=(1,1)$

EF: $E=(4,4)\\F=(6,2)$

Now that we have our points we can use the slope formula to prove these two line have the same slope and are therefore parallel to eachother:

$\frac{y_1-y_2}{x_1-x_2}$ = Slope Formula

BC = $\frac{4-1}{-2-1} =\frac{3}{-3} =\frac{-3}{3} =-1$

EF = $\frac{4-2}{4-6} =\frac{2}{-2}=\frac{-2}{2}= -1$

So now we proved that both of these lines have a slope of -1. Then we can use the slope intercept formula and one of the points from the line EF to find the y-intercept of the of line EF:

Let's use point = $(4,4)$

$y=4,m=-1,x=4,b=?$

$y=mx+b\\4=-1(4)+b\\4=-4+b\\(+4) 4=-4+b(+4)\\8=b$

We used the formula and found that the y-intercept was $(0,8)$ , so now we plug in all of our answers:

$y=-1x+8$

This is the complete answer but if you wanted to simplify it more you could write it as $y=-x+8$ , cause as long as you make the x negative in the equation it will always be as if you multiplied it by -1.