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)

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.