See explanations below
Step-by-step explanation:
Chanel
(i) 90° counterclockwise and then dilation by a factor of 1/2
Trapezoid PQRS is given as :
P(6,-4) -------P'(4,6)
Q(2,-2)------Q'(2,2)
R(2,-6)-------R'(6,2)
S(6,-6)-------S'(6,6)
The transformation switches the position of (x,y) to and adds a -ve sign to the original y value
B. The new coordinates are : P'(4,6), Q'(2,2),R'(6,2) and S'(6,6)
The rule for rotation 90° counterclockwise about the origin is (x,y)⇒(-y,x)
The rule for dilation with scale factor of 1/2 is (x,y)------(1/2x,1/2y)
P'(4,6) -----P''(2,3)
Q'(2,2)-----Q''(1,1)
R'(6,2)-----R''(3,1)
S'( 6,6)-----S''(3,3)
The dilation reduces the coordinates by 1/2
Preston
E. (i)Reflection over x-axis where the rule is : (x,y)----(x,-y)
(ii)Dilation by scale factor of 1/2 the rule is : (x,y)---(1/2x, 1/2y)
Applying reflection over x-axis rule;
P(6,-4) -----P'(6,4)
Q(2,-2)-----Q'(2,2)
R(2,-6)------R'(2,6)
S(6,-6)------S'(6,6)
The coordinates have changed in that a negative sign is added to the y-axis coordinate.
F. P'(6,4), Q'(2,2), R'(2,6) and S'(6,6)
G. Applying the dilation by scale factor of 1/2
P'(6,4)-------P''(3,2)
Q'(2,2)------Q''(1,1)
R'(2,6)------R''(1,3)
S'(6,6)------S''(3,3)
The coordinates of P'Q'R'S are divide by 2 to give coordinates of P''Q''R''S''
Comparing the answers to the final figure given
K(3,2)
L(1,1)
M(1,3)
N(3,3)
Preston is correct because his sequence proves trapezoid PQRS is similar to trapezoid KLMN.
Learn More
Reflection and dilation :brainly.com/question/13408902
Keywords :trapezoid, maps, rotate, counterclockwise, dilate,reflect,scale factor,shape, coordinate
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