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1 year ago

What is an equation of the line that passes through the points (5,-6) and (-5,-4)??

Mathematics

1 answer:

Brums [2.3K]1 year ago

6 0

The linear equation that passes through the points (5,-6) and (-5,-4) is:

y = (-1/5)*x + 5

<h3>How to find the equation of the line?</h3>

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here the line passes through (5, -6) and (-5, -4) then the slope is:

a = (-4 + 6)/(-5 - 5) = -2/10 = -1/5

So the line is something like:

y = (-1/5)*x + b

Replacing the values of the point (5, -6) in the equation we get:

-6 = (-1/5)*5 + b

-6 = -1 + b

-6 + 1 = b

5 = b

The linear equation is:

y = (-1/5)*x + 5

Learn more about linear equations:

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You might be interested in

Given the midpoint and one endpoint of a line segment, find the other endpoint.

neonofarm [45]

Answer:

(-12 , 2)

Step-by-step explanation:

GIVEN :-

Co-ordinates of one endpoint = (-4 , -10)
Co-ordinates of the midpoint = (-8 , -4)

TO FIND :-

Co-ordinates of another endpoint.

FACTS TO KNOW BEFORE SOLVING :-

Section Formula :-

Let AB be a line segment where co-ordinates of A = (x¹ , y¹) and co-ordinates of B = (x² , y²). Let P be the midpoint of AB . So , by using section formula , the co-ordinates of P =

$(x , y) = (\frac{x^2 + x^1}{2} ,\frac{y^2 + y^1}{2} )$

PROCEDURE :-

Let the co-ordinates of another endpoint be (x , y)

So ,

$(-8 , -4) = (\frac{-4 + x}{2} , \frac{-10 + y}{2} )$

First , lets solve for x.

$=> \frac{x - 4}{2} = -8$

$=> x - 4 = -8 \times 2 = -16$

$=> x = -16 + 4 = -12$

Now , lets solve for y.

$=> \frac{y - 10}{2} = -4$

$=> y - 10 = -4 \times 2 = -8$

$=> y = -8 + 10 = 2$

∴ The co-ordinates of another endpoint = (-12 , 2)

3 0

3 years ago

Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2, 2). Which statement is true about the dilation?

arsen [322]

Answer:

Option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Step-by-step explanation:

As the assumption quadrilateral ABCD is shown in figure a.

First located the center of the dilation which is located at (2,2) as shown in figure b.

The next thing we want to do is to determine the distance of the center of dilation to each of the points of quadrilateral ABCD as shown in figure b.

Let’s just start with the distance from the center to the point A, but notice we don’t have to move up and down in y direction. So, what we have to do is to increase this by the factor 2. Because this horizontal distance is 1 i.e. the distance from dilation center (2,2) to point A, we just have to multiply by 2 which would be a distance of 2 and this point right here will be the new location of point A’ (0,2).

And the distance from the center to the point C is the horizontal distance of 2 i.e. the distance from dilation center (2,2) to point C, we just have to multiply by 2 which would be a distance of 4 and this point right here will be the new location of point C’ (6,2).

And the distance from the center to the point B is the upward vertical distance of 1 i.e. the distance from dilation center (2,2) to point B, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point B’ (2,4).

And similarly the distance from the center to the point D is the downward vertical distance of 1 i.e. the distance from dilation center (2,2) to point D, we just have to multiply by 2 which would be a vertical distance of 2 and this point right here will be the location of point D’ (2,0).

So, Quadrilateral A'B'C'D' is dilated by a scale factor of 2 centered around (2, 2).

Just notice in figure b that the segment B'D' will run through (2,2) and will be longer than the segment BD.

So,option (B) is true i.e segment B'D' will run through (2,2) and will be longer than the segment BD.

Learn more about dilation from brainly.com/question/12528454

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