Question

XYZ with vertices X (1,1), Y (3,5), Z (5,1) with rotated 180 degrees about the origin. What will be the coordinates of Y'?

Answer 1

Answer:

(-3, -5)

Step-by-step explanation:

When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is

The new position of the point Y (3, 5) will be Y' (-3, -5)

Answer 2

Given: XYZ with vertices $X(1,1),Y(3,5),Z(5,1)$

To find: The coordinates of $Y'$ when the vertices are rotated $180^o$

Solution:

The given vertices are:

$X(1,1)\\Y(3,5)\\Z(5,1)$

The values of the vertices show that the points lie on the first quadrant where the values are positive.

When the coordinates are rotated at an angle of $180^o$ the points are moved towards the fourth quadrant where the values are all negative.

The points can be represented as:

$X(1,1)$ → $X(-1,-1)$

$Y(3,5)$ → $Y(-3,-5)$

$Z(5,1)$ → $Z(-5,-1)$

It is observed that the values are just a compliment of the given vertices. Hence when coordinates are rotated at an angle of $180^o$ they give us the compliment of the values.

Final answer:

The coordinates of Y' when the vertices are rotated at an angle of $180^o$ is $Y'(-3,-5)$