I found the
figure and take advantage to
attache it for any reference.
Answer: c. Reflection across the x-axis, followed by translation 10 units right Explanation:1) The
vertices of
figure 1 are:
(-3, 4); (-4, 7); (-5, 2); (-6, 5)2) The
vertices of
figure 2 are: (
7, - 4); (6, -7); (5, -2); (4, -5)3) Since, many sets of two transformations can transform the figure 1 into the figure 2, you need to
probe each pair of the choice statements.
4) This proves that the statements of the
option C. yield the figure 2:1) Reflection across the x-axis.A reflection across the x-axis, keeps the x-coordinate, and change the y-coordinate to its opposite (negative). This is:
(x, y) → (x - y).Use that rule on the 4 vertices of the figure 1 and you get:
(-3, 4) → (-3, -4);
(-4, 7) → (-4, -7);
(-5, 2) → (-5, -2);
(-6, 5) → (-6, -5)
2) Translation 10 units rightA translation of 10 units transforms the points (x,y) into (x + 10, y):
(x,y) → (x + 10), y)Apply that rule:
(-3, -4) → (-3 + 10, -4) = (7, -4)
(-4, -7) → (-4 + 10, 7) = (6, -7)
(-5, -2) → (-5 + 10, -2) = (5, -2)
(-6, -5) → (-6 + 10, -5) = (4, - 5)
Then, it has been proven that the two transformations given in the option C. transforms figure 1 onto figure 2.