Notice that the reflection is over a line of the form x=constant; in this case, the y-coordinate of the reflected point stays the same while the x-coordinate changes as expressed by the transformation below

$\begin{gathered} y\rightarrow y \\ x\rightarrow2a+x \\ where \\ x=a\rightarrow\text{ vertical line} \end{gathered}$

Hence, in our case

$\Rightarrow(x,y)=(2*-4-x,y)=(-8-x,y)$

Transform points N, M, and O accordingly,

$\begin{gathered} \Rightarrow N^{\prime}=(-8-(-5),2)=(-8+5,2)=(-3,2) \\ \Rightarrow M^{\prime}=(-8-(-2),1)=(-6,1) \\ \Rightarrow O^{\prime}=(-8-(-3),3)=(-5,3) \end{gathered}$ <h2>Therefore, the answer is the first option (top to bottom)</h2>

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1 year ago

Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

Thepotemich [5.8K]

Answer:

Length of side of rhombus is $x=\frac{ab}{a+b}$

Step-by-step explanation:

Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.

It is also given that AB=a and AC=b

Let side of rhombus is x.

In ΔCEF and ΔCBA

∠CEF=∠CBA (∵Corresponding angles)

∠CFE=∠CAB (∵Corresponding angles)

By AA similarity rule, ΔCEF~ΔCBA

∴ their sides are in proportion

$\frac{EF}{AB}=\frac{CF}{AC}$