Triangle ABC has coordinates A(-1, -3), B(-1, -2), and C(-5, -3). If the triangle is rotated 180° clockwise about the origin, what are the coordinates of A'?
just change the sign of every coordinate
To rotate a point about the origin by 180° clockwise, you need to switch the signs of both the x and y coordinates.
Let's apply this to point A(-1, -3):
To switch the sign of the x-coordinate, we change -1 to 1.
To switch the sign of the y-coordinate, we change -3 to 3.
Therefore, the coordinates of A' after rotating the triangle 180° clockwise about the origin are A'(1, 3).
To rotate a point (x, y) 180° clockwise about the origin, we can use the following formulas:
x' = x * cos(180°) - y * sin(180°)
y' = x * sin(180°) + y * cos(180°)
Since cos(180°) = -1 and sin(180°) = 0, we can simplify the formulas to:
x' = -x
y' = -y
Let's find the coordinates of A' by substituting the values:
x' = -(-1) = 1
y' = -(-3) = 3
Therefore, the coordinates of A' are (1, 3).