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2 years ago

7

How do you find the point-slope formula for this problem? (-1,7); m= -4

1 answer:

Nadya [2.5K]2 years ago

7 0

Answer:

y-7 = -4(x+1)

Step-by-step explanation:

The point slope formula is

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y-7 = -4(x--1)

y-7 = -4(x+1)

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

<u>Explanation:</u>

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

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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;

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

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

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

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.

$2y-1=5$

$2y=5+1$

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