Consider the composite function (g (x) ) = StartRoot StartFraction 1 Over x squared minus 3 EndFraction EndRoot.
2 answers:
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J (-4, 1), K (-4, -2), L (-3, -1)
(a) To rotate a point 90° counterclockwise about the origin, multiply the y-coordinate by -1 and then interchange the z- and y- coordinates.
(x, y)'' = (-y, x)
Substitute all of J (-4, 1), K (-4, -2), L (-3, -1) for (x, y)
Solution:
J'' = J (-4, 1) × (x, -1) = (-4, -1)
K'' = K (-4, -2) × (x, -1) = (-4, 2)
L'' = L (-3, -1) × (x, -1) = (-3, 1)
J'' (-1, -4), K'' (2, -4), L'' (1, -3)
Image ▲J"K"L": Look at the first attached picture.
(b) To reflect a point in the y-axis, we multiply its x-coordinate by -1.
Substitute all of J (-4, 1), K (-4, -2), L (-3, -1) for (x, y)
Multiplying by -1:
J'' = J (-4, 1) × (-1, y) = (4, 1)
K'' = K (-4, -2) × (-1, y) = (4, -2)
L'' = L (-3, -1) × (-1, y) = (3, -1)
J'' (4, 1), K'' (4, -2), L'' (3, -1)
Image ▲J"K"L": Look at the second attached picture.
