a) The length of AB is 6units
b) The image segment AB under the transformation (x, y) — (x, 2y) are reflections of each other since the x coordinate is constant and y coordinates are negative of each other.
c) The image segment AB under the transformation (x, y) — (x+2, y) are reflections of each other since the x coordinate is constant and y coordinates are negative of each other.
d) The two transformations both lie between the 1st and the 4th quadrant of the graph but the magnitude of transformation in (b) is more than that of (c)
a) The formula for calculating the distance between two points is expressed as;
[tex]D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Given the points A(2, 3) and B(2, -3).
substitute the given values into the formula:
[tex]D =\sqrt{(-3-3)^2+(2-2)^2}\\D=\sqrt{(-6)^2+0^2}\\D=\sqrt{36}\\D =6\\[/tex]
Hence the length of AB is 6units
b) The transformation (x, y) — (x, 2y) means that the y-coordinate was dilated by 2 units. Dilating coordinate A (2, 3)
A' = (2, 2(3))
A' = (2, 6)
For coordinate B (2, -3), the translation is expressed as:
B' = (2, 2(-3))
B' = (2, -6)
Hence the image segment AB under the transformation (x, y) — (x, 2y) are reflections of each other since the x coordinate is constant and y coordinates are negative of each other.
c) The transformation (x, y) — (x+2, y) means that the x-coordinate was translated to the right by 2 units. Translating coordinate A (2, 3)
A' = (2+2, 3)
A' = (4, 3)
For coordinate B (2, -3), the translation is expressed as:
B' = (2+2, -3)
B' = (4, -3)
The image segment AB under the transformation (x, y) — (x+2, y) are reflections of each other since the x coordinate is constant and y coordinates are negative of each other.
d) The two transformations both lie between the 1st and the 4th quadrant of the graph but the magnitude of transformation in (b) is more than that of (c)
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