The coordinates of the vertices of △JKL are J(1, 4) , K(6, 4) , and L(1, 1) . The coordinates of the vertices of △J′K′L′ are J′(0, −4) , K′(−5, −4) , and L′(0, −1) .

What is the sequence of transformations that maps △JKL to △J′K′L′ ?

reflection across the x-axis

rotation of 180° about the origin

rotation of 90° counterclockwise about the origin

translation 1 unit left

A sequence of transformations that maps △JKL to △J′K′L′ is a followed by a ?

The sequence of transformations are;

A translation by 1 unit left, followed by a reflection across the x-axis

Step-by-step explanation:

Here, we want to know the transformation sequence

Let us select one point

J(1,4)

to J’(0,-4)

To translate 1 unit right means that we are subtracting the value of 1 from the x-coordinate

That leaves us with (0,4)

To get the change in the y-coordinate value to negative, it means that we have reflected over the x-axis

x-axis reflection turns (x,y) to (x,-y)

So, the sequence of transformations that maps the two is;

A translation by 1 unit left followed by a reflection across the x-axis

translation 1 unit left, then 180 degrees

Step-by-step explanation:

J (1,4)

K (6,4)

L (1,1)

Moving it 1 unit left,  x unit - 1

J (0,4)

K (5,4)

L (0,1)

Now, rotate it 180 degrees, (x,y) = (-x,-y)

J' (0,-4)

K' (-5,-4)

L' (0,-1).

Hence, the triangle JKL is transformed into triangle J'K'L' when a triangle JKL translates 1 unit to the left and then rotate 180 degrees about the origin.

except a rational number. : )