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3 years ago

Which transformation shows a reflection of ΔDEF?

Mathematics

2 answers:

Helen [10]3 years ago

8 0

Answer:

The image B with purple figures is correct.

Step-by-step explanation:

We are given the figure DEF and we are required to find the figure which is obtained after reflecting it.

Now, reflection of a figure means to flip the figure over a line.

In the green figure, the points D and E are interchanged which is not possible in reflection.

In the blue figure, there is no change.

In the purple figure, the triangle is flipped over the line DE and so it is the correct answer.

Hence, the purple figure is obtained after reflecting the figure DEF.

m_a_m_a [10]3 years ago

7 0

The answer is B or the purple one

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$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 2) and (6, 3):

$m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}$

Therefore, the slope of the line is $\frac{\displaystyle 1}{\displaystyle 7}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

Plug in one of the given points and solve for b:

$2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b$

Add $\frac{\displaystyle 1}{\displaystyle 7}$ to both sides to isolate b:

$2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b$

Therefore, the y-intercept of the line is $\frac{\displaystyle15}{\displaystyle 7}$ . Plug this back into $y=\frac{\displaystyle 1}{\displaystyle 7}x+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

I hope this helps!

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