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=

Answers: 1

Show answers

Answers

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:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 | - 4 (rewriting in general form)

y = | x - (- 3) | - 4

the "-4 " term means that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

Which of the following functions is graphed below?

Answer from: Quest

Iagree that is the answer to the question
Can someone me do my homework !

Another question on Mathematics

Mathematics, 21.06.2019 23:00

Frank has a devised a formula for his catering business that calculates the number of meatballs he needs to prepare. the formula is m=4a+2c, where c=number of children; m=number of meatballs; a=number of adults. how many meatballs are required for a party of 10 adults and 5 children?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

Find │–14│ a. 14 b. –14 c. start fraction 1 over 14 end fraction

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Mrs. blake's bill at a restaurant is $42.75. she wants to leave the waiter an 18% tip. how much will she pay in all, including the tip?

Answers: 2

Answer

Mathematics, 22.06.2019 00:50

Acube has a volume of 800 cubic inches. whatis the length of an edge of the cube, in inches? a. 23/100b. 43/50c. 83/100d. 1003/2e. 1003/8