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Rina8888 [55]
3 years ago
13

A dilation with a scale factor of 15 and centered at the origin is applied to MN¯¯¯¯¯¯¯ with endpoints M(−2, −4) and N(1, 5) .

Mathematics
2 answers:
Nutka1998 [239]3 years ago
5 0
<span>coordinates m' is going to be (-2/5,-4/5)


</span><span>coordinates n' is going to be (1/5,1)

</span>I just took the test i hope this helps!
777dan777 [17]3 years ago
3 0

Answer:

(-2/5, -4/5); (1/5, 1)

Step-by-step explanation:

We multiply the x- and y-coordinates of both points by the scale factor, 1/5:

M' = (-2(1/5), -4(1/5)) = (-2/5, -4/5)

N' = (1(1/5), 5(1/5)) = (1/5, 5/5) = (1/5, 1)

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In the figure below

1) Using the theorem of similar triangles (ΔBXY and ΔBAC),

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Where

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Thus,

\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}

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2) BX = 9, BA = 15, BY = 15, YC = y

In the above diagram,

\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}

Thus, from the theorem of similar triangles,

\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}

solving for y, we have

\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}

thus, YC = 10.

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Pls help!!
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