Tricia plotted the point (4,2) on a coordinate plane. She then performed a series of

transformations on the point so that the point mapped onto its original location of (4,2). Sort

the transformations below so that (4, 2) maps onto itself by the end of the last transformation.

Write the correct transformation for each step.

Translation 2 units left and 1 unit down

Translation 2 units right and 3 units up

Transa

mel

Rotation of 180° about the origin

Reflection over the y-axis

Rotation

a) the correct transformation is (2,1)

b) the correct transformation is (6,5)

c) reflection over y- axis is (-4,2)

Step-by-step explanation:

we will use below conditions

Type of transformation                                  change to co-ordinate point

i) Vertical translation up 'd' units                     (x, y) changes to (x, y +d)

ii) Vertical translation down 'd' units                (x, y) changes to (x, y -d)

iii) horizontal translation left 'c' units                (x, y) changes to (x- c, y )

iv)  horizontal translation right 'c' units             (x, y) changes to (x+ c, y )

iv) Reflection over 'x' axis                                  (x, y)  changes to (x , -y)

v) Reflection over 'y' axis                                    (x, y)  changes to (-x , y)

now given data the original location is (4,2)

a) given data is translation '2'units left and one unit down

now we will use above conditions (iii) and (ii)

Answer:- given translation is '2' units left that is (4-2,2) and

again this is translation one unit down that is (4-2,2-1).

There fore the correct transformation is (2,1)

b) given data is translation '2'units right and '3' units up.

now we will use above conditions (iv) and (i)

Answer:- given translation is '2' units right that is (4+2,2) and

again this is translation three units up that is (4+2,2+3).

There fore the correct transformation is (6,5)

c) Reflection over 'y' - axis that is (-4,2)  ( use condition is (v).

Final answers:-

a) the correct transformation is (2,1)

b) the correct transformation is (6,5)

c) reflection over y- axis is (-4,2)

the answer will be the last one

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.