Question

Suppose the equation of line s is y = 2. What are the coordinates of C' of ΔA'B'C' for Rs?

The graph with X-coordinate marks -4, 0, 4 and Y-coordinate mark -4, -1, 0, and 4. The triangle ABC with coordinates A at (-1, 1), B at (1, -1), C at (-3, -1).

Answer 1

Answer:

C'(-3,5)

Step-by-step explanation:

Given triangle ABC with vertices at points A(-1, 1), B(1, -1), C(-3, -1).

Line s with equation y = 2 is the line of reflection.

The reflection across the line s has the rule

$(x,y)\rightarrow (x,4-y)$

According to this rule:

• $A(-1,1)\rightarrow A'(-1,3);$
• $B(1,-1)\rightarrow B'(1,5);$
• $C(-3,-1)\rightarrow C'(-3,5).$

Answer 2

When a shape is reflected, it must be reflected across a line.

The coordinates of C' is (-3,5)

The coordinates of the triangle are:

$A=(-1,1)$

$B=(1,-1)$

$C=(-3,-1)$

The rule of reflection across line y = 2 is:

$(x,y) = (x,4-y)$

So, we have:

$A' = (-1,4-1)$

$A' = (-1,3)$

$B' = (1,4--1)$

$B' = (1,5)$

$C' = (-3,4--1)$

$C' = (-3,5)$

Hence, the coordinates of C' is (-3,5)

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