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Natalija [7]
3 years ago
8

Line l has the equatin y= 1/3x. Find the equation of the image l after a dilation with a scale factor of 1/2, centered at the or

igin.

Mathematics
2 answers:
Romashka [77]3 years ago
4 0

Answer:

sssssssssssssssssssssssssssssssss

Step-by-step explanation:

HACTEHA [7]3 years ago
3 0

Answer:

y = \frac{1}{3} x + \frac{8}{3}

Step-by-step explanation:

The equation of the line I is  y = \frac{1}{3} x

Scale factor = \frac{1}{2}, center = (0, 0)

To find the dilated line, we need follow the steps below:

Step 1: Draw the equation of the given line I

Step 2: Let's take a point from the line.

Let's take (2, 6) which is on the line I.

Let's find the dilated point by the scale factor  \frac{1}{2}

Multiply the point (2, 6) by  \frac{1}{2}, we get

(2.\frac{1}{2} , 6.\frac{1}{2} ) = (1, 3)

Step 3: Write the equation of the new line (Image I)

The dilated line has the same slope.

So slope (m) =  \frac{1}{3}

x = 1 and y = 3

Now let's find the slope intercept.

y = mx + b

Plug in x = 1, y = 3 and slope (m) =  \frac{1}{3}

3 =  \frac{1}{3}.1 + b

3 = \frac{1}{3} + b

b = 3 - \frac{1}{3}

b = \frac{3.3 -1}{3} = \frac{9 -1}{3} = \frac{8}{3}

Now let's find the equation of the image I.

y = mx + b

y = \frac{1}{3} x + \frac{8}{3}

The required equation is y = \frac{1}{3} x + \frac{8}{3} after the dilation of scale factor.

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Step-by-step explanation:

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