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irina1246 [14]
3 years ago
12

Activity 2. Find the equation of the line using Two-Point form,

Mathematics
1 answer:
jasenka [17]3 years ago
3 0

Answer:

1) equation of line is: y-3=0

2) equation of line is: \mathbf{y-3=-\frac{1}{2}(x-4)}

3) equation of line is: \mathbf{y+3=-\frac{4}{3}(x-3}

4) equation of line is: \mathbf{y-2=-2(x-2)}

Step-by-step explanation:

We need to find the equation of the line using Two-Point form.

The general equation of two-point form is: y-y_1=m(x-x_1) where m is slope.

The formula used to calculate slope is: Slope=\frac{y_2-y_1}{x_2-x_1}

1. (1,3) and (-2,3)

First finding slope

We have: x_1=1, y_1=3, x_2=-2, y_2=3

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{3-3}{-2-1}\\Slope=\frac{0}{-3}\\Slope=0\\

So, equation of line will be:

Using slope m=0 and point (1,3)

y-y_1=m(x-x_1)\\y-3=0(x-1)\\y-3=0\\

So, equation of line is: y-3=0

2. (4,3) and (6,2)

First finding slope

We have:x_1=4, y_1=3, x_2=6, y_2=2

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{2-3}{6-4}\\Slope=\frac{-1}{2}\\

So, equation of line will be:

Using slope m=\frac{-1}{2} and point (4,3)

y-y_1=m(x-x_1)\\y-3=\frac{-1}{2}(x-4)\\y-3=-\frac{1}{2}(x-4)

So, equation of line is: \mathbf{y-3=-\frac{1}{2}(x-4)}

3) (3,-3) and (0,1)

First finding slope

We have: x_1=3, y_1=-3, x_2=0, y_2=1

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{1-(-3)}{0-3}\\Slope=\frac{1+3}{-3}\\Slope=-\frac{4}{3}\\

So, equation of line will be:

Using slope m=-\frac{4}{3} and point (3,-3)

y-y_1=m(x-x_1)\\y-(-3)=-\frac{4}{3}(x-3)\\y+3=-\frac{4}{3}(x-3)\\

So, equation of line is: \mathbf{y+3=-\frac{4}{3}(x-3)}

4) (2,2) and (4,-2)

First finding slope

We have: x_1=2, y_1=2, x_2=4, y_2=-2

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-2}{4-2}\\Slope=\frac{-4}{2}\\Slope=-2\\

So, equation of line will be:

Using slope m=-2 and point (2,2)

y-y_1=-2(x-x_1)\\y-2=-2(x-2)\\

So, equation of line is: \mathbf{y-2=-2(x-2)}

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The value of <u>ML = 3</u>, using the mid-point theorem of triangles.

According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."

In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.

Thus, by the midpoint theorem, we can say that:

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Assuming AB = BC = AC = x units, we get:

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Thus, the triangle LMN is an equilateral triangle.

Thus, MN = ML = NL.

Given MN = 3, we can write the value of ML = 3.

Thus, the value of <u>ML = 3</u>, using the mid-point theorem of triangles.

Learn more about the mid-point theorem of triangle at

brainly.com/question/9635025

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"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"

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