Question

question #21
the triangle below will be rotated 90 degrees counterclockwise about point a.
what will be the new coordinates of point c?
a (1, 4)
b (2, 4)
c (3, 2)
d (6, 8)

Explanation:

Step1: Identify coordinates of points

Point $A$: $(2, 3)$, Point $C$: $(3, 4)$

Step2: Find relative coordinates of $C$ to $A$

Subtract $A$'s coordinates from $C$'s:
$\Delta x = 3 - 2 = 1$, $\Delta y = 4 - 3 = 1$

Step3: Apply 90° counterclockwise rotation rule

For rotation about a point, relative coordinates transform as $(\Delta x, \Delta y) \to (-\Delta y, \Delta x)$
New relative coordinates: $(-1, 1)$

Step4: Calculate new coordinates of $C$

Add new relative coordinates to $A$'s coordinates:
$x = 2 + (-1) = 1$, $y = 3 + 1 = 4$

Answer:

A. (1, 4)