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What is the ordered pair of [tex]M^{\prime}[/tex] after point [tex]M(5,6)[/tex] is rotated [tex]90^{\circ}[/tex] counterclockwise?

A. [tex]M^{\prime}(-6,5)[/tex]
B. [tex]M^{\prime}(6,-5)[/tex]
C. [tex]M^{\prime}(5,-6)[/tex]
D. [tex]M^{\prime}(-5,6)[/tex]

Sagot :

GinnyAnsweridn
To determine the ordered pair of [tex]\( M' \)[/tex] after rotating point [tex]\( M(5, 6) \)[/tex] 90 degrees counterclockwise, we can follow the standard rotation transformation rules. When a point [tex]\((x, y)\)[/tex] is rotated 90 degrees counterclockwise about the origin, the new coordinates [tex]\((x', y')\)[/tex] are given by:

[tex]\[ x' = -y \][/tex]
[tex]\[ y' = x \][/tex]

Given the original coordinates of point [tex]\( M \)[/tex] as [tex]\( (5, 6) \)[/tex]:

1. Identify [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- [tex]\( x = 5 \)[/tex]
- [tex]\( y = 6 \)[/tex]

2. Apply the transformation rules:
- [tex]\( x' = -y = -(6) = -6 \)[/tex]
- [tex]\( y' = x = 5 \)[/tex]

Therefore, the coordinates of the point [tex]\( M' \)[/tex] after the 90-degree counterclockwise rotation are [tex]\( (-6, 5) \)[/tex].

Hence, the ordered pair of [tex]\( M' \)[/tex] is [tex]\( \boxed{(-6, 5)} \)[/tex].
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