Question

Write an equation of the line that is perpendicular to the line y = 2x + 8, and which passes through the point (6,-2).

A) y = 2x + 4
B) y = -2x + 1
C) y = -1/2x + 1
D) y = -1/2x + 1

A triangle is drawn and then translated as shown in the diagram. Which statement is true?
A) The two triangles are congruent because all rectangles are congruent.
B) The two triangles are not congruent because a translation changes side length.
C) The two triangles are not congruent because a translation changes angle measures.
D) The two triangles are congruent because a translation does not change size and shape.

Answer 1

D. The two triangles are congruent because a translation does not change size and shape.

Explanation:

I'm pretty sure that D is the answer. It jut basically moved , didn't change anything.

Answer 2

1. The equation of line is
`y=-(1)/(2)(x)+1`.

2. The correct option is D.

Explanation:

1.

The slope intercept form of a line is

`y=mx+b`

Where, m is slope and b is y-intercept.

The given equation of a line is

`y=2x+8`

The slope of line is 2 and y-intercept is 8.

The product of slopes of two perpendicular lines is -1.

`m_1* m_2=-1`

`2* m_2=-1`

`m_2=-(1)/(2)`

The slope of required line is
`-(1)/(2)` and it passes through the point (6,-2).

The equation of required line is

`y-y_1=m(x-x_1)`

`y+2=-(1)/(2)(x-6)`

`y+2=-(1)/(2)(x)+3`

`y=-(1)/(2)(x)+3-2`

`y=-(1)/(2)(x)+1`

Therefore the equation of line is
`y=-(1)/(2)(x)+1`.

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.