Rectangle ABCD is congruent to rectangle .
2 answers:
Answer:- A. Rectangle ABCD was translated 8 units left and then 7 units down.
Explanation:-
We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".
i.e.(2-8,4-7)=(-6,-3)
Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"
B (2,2) → B" (-6,-5)
C (6,2) → C" (-2,-5)
D(6,4) → D" (-2,-3)
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Given:
The scale factor is and the center of dilation is at the point (4,2).
Red is original figure and green is dilated figure.
To find:
The coordinates of point C' and point A.
Solution:
Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
According to the given information, the scale factor is and the center of dilation is at (4,2).
...(i)
Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using (i), we get
Therefore, the coordinates of Point C' are C'(2,5).
We assumed that point A is A(m,n).
Using (i), we get
From the given figure it is clear that the image of point A is (8,4).
On comparing both sides, we get
And,
Therefore, the coordinates of point A are (16,8).