Mathematics, 29.01.2021 18:00 ehaynie

Please helppp, I'm using all my points!! Line A passes through the points (-3,-4) and (-6,-5). Write the equation of the image of A after a dilation with a scale factor of 2. Write your in answer in slope-intercept form. y=

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Answer from: sophiapknight

The equation of the image of A after a dilation with a scale factor of 2 will be:

$y\:=\:\frac{1}{3}x\:-6$

Step-by-step explanation:

Some background Knowledge about dilation.

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

If the scale factor > 1, the image is enlargedIf the scale factor is between 0 and 1, it gets shrunkIf the scale factor = 1, the object and the image are congruent

Rule to calculate the dilation by a scale factor 2 centered at the origin

P(x, y) → P'(2x, 2y)

Here, P'(2x, 2y) is the image of P(x, y).

It means the coordinates of the image can be determined by multiplying the coordinates of the original point by 2.

Now, let us solve our case:

Given the points

(-3, -4)(-6, -5)

Let say the points are X(-3, -4) and Y(-6, -5)

Rule to calculate the dilation by a scale factor 2 centered at the origin

P(x, y) → P'(2x, 2y)

X(-3, -4) → X' (2(-3), 2(-4)) → X'(-6, -8)

Y(-6, -5) → Y' (2(-6), 2(-5)) → Y'(-12, -10)

Thus, after the dilation scale of factor 2, now the image line will through the points X'(-6, -8) and Y'(-12, -10)

so we have the points of the image line

X'(-6, -8)Y'(-12, -10)

Determining the slope between X'(-6, -8) and Y'(-12, -10)

$\left(x_1,\:y_1\right)=\left(-6,\:-8\right),\:\left(x_2,\:y_2\right)=\left(-12,\:-10\right)$

$m=\frac{-10-\left(-8\right)}{-12-\left(-6\right)}$

$m=\frac{1}{3}$

The slope-intercept form of the line equation

y = mx+b

where

m is the slopeb is the y-intercept

now substituting m = 1/3 and (-6, -8) in the slope-intercept form of the line equation

y = mx + b

$-8\:=\:\frac{1}{3}\left(-6\right)\:+\:b$

-2+b=-8

Add 3 to both sides

-2+b+2=-8+2

Simplify

b=-6

now substituting b = -6 and m = 1/3 in the slope-intercept form of line equation

y = mx + b

$y\:=\:\frac{1}{3}x\:+\:\left(-6\right)$

$y\:=\:\frac{1}{3}x\:-6$

Therefore, the equation of the image of A after a dilation with a scale factor of 2 will be:

$y\:=\:\frac{1}{3}x\:-6$

Answer from: Quest

step-by-step explanation:

the multiplicative inverse of a fraction a/b is b/a. for the multiplicative inverse of a real number, divide 1 by the number. for example, the reciprocal of 5 is one fifth 1/5 or 0.2, and the reciprocal of 0.25 is 1 divided by 0.25, or 4.

Answer from: Quest

only 10/60 isn't equivalent

hope this : )

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Please helppp, I'm using all my points!! Line A passes through the points (-3,-4) and (-6,-5). Write...