Answer:
1. The equation of line is
.
2. The correct option is D.
Step-by-step explanation:
1.
The slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is slope and b is y-intercept.
The given equation of a line is
![y=2x+8](https://tex.z-dn.net/?f=y%3D2x%2B8)
The slope of line is 2 and y-intercept is 8.
The product of slopes of two perpendicular lines is -1.
![m_1\times m_2=-1](https://tex.z-dn.net/?f=m_1%5Ctimes%20m_2%3D-1)
![2\times m_2=-1](https://tex.z-dn.net/?f=2%5Ctimes%20m_2%3D-1)
![m_2=-\frac{1}{2}](https://tex.z-dn.net/?f=m_2%3D-%5Cfrac%7B1%7D%7B2%7D)
The slope of required line is
and it passes through the point (6,-2).
The equation of required line is
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
![y+2=-\frac{1}{2}(x-6)](https://tex.z-dn.net/?f=y%2B2%3D-%5Cfrac%7B1%7D%7B2%7D%28x-6%29)
![y+2=-\frac{1}{2}(x)+3](https://tex.z-dn.net/?f=y%2B2%3D-%5Cfrac%7B1%7D%7B2%7D%28x%29%2B3)
![y=-\frac{1}{2}(x)+3-2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7D%28x%29%2B3-2)
![y=-\frac{1}{2}(x)+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7D%28x%29%2B1)
Therefore the equation of line is
.
2.
Translation is a rigid transformation. It means if a figure translated then the image and preimage are congruent
It the given figure two triangles are congruent because a translation does not change size and shape.
Therefore the correct option is D.