Question

PLEASEE HELPP!

Answer 1

Transformation involves changing the position of a shape

• The sequence that maps ∆ABC to ∆A′B′C′ is reflection across the y-axis, followed by horizontal and vertical shifts
• The ordered pair rule is: $(x,y) \to (-x,-1,y-2)$

(a) The sequence that maps both triangles

From the figure the coordinates of both triangles are:

$A = (-5,0)$

$B = (-2,1)$

$C = (-4,2)$

$A' = (4,-2)$

$B' = (1,-1)$

$C = (3,0)$

Start by reflecting triangle ABC across the y-axis.

The rule of this transformation is:

$(x,y) \to (-x,y)$

So, we have:

$A = (5,0)$

$B = (2,1)$

$C = (4,2)$

Next, translate the triangle 1 unit left and 2 units down

The rule of this transformation is:

$(x,y) \to (x,-1,y-2)$

So, we have:

$A' = (4,-2)$

$B' = (1,-1)$

$C = (3,0)$

Hence, the sequence that maps ∆ABC to ∆A′B′C′ is reflection across the y-axis, followed by horizontal shift to the left by 1 unit, and vertical shift down by 2 units

(b) The ordered pair rule

In (a), we have:

$(x,y) \to (-x,y)$ ---- reflection

$(x,y) \to (x,-1,y-2)$ --- translation

Combine both transformations, so we have the following ordered pair:

$(x,y) \to (-x,-1,y-2)$

Hence, the ordered pair rule is: $(x,y) \to (-x,-1,y-2)$

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