Triangle LMN is drawn with vertices at L(−4, −1), M(0, −1), N(−4, −3). Determine the image vertices of L′M′N′ if the preimage is rotated 90° clockwise.

Question

L′(4, 1), M′(0, 1), N′(4, 3)
L′(−4, −1), M′(0, −1), N′(−4, −3)
L′(−1, 4), M′(−1, 0), N′(−3, 4)
L′(1, −4), M′(1, 0), N′(3, −4)

Answer 1

To find the image vertices of triangle LMN after a 90° clockwise rotation, we can use the rule for rotating points on the Cartesian plane.

When rotating a point \((x, y)\) 90° clockwise, the new coordinates become \((y, -x)\).

Let's apply this to the vertices of triangle LMN:

1. Vertex L(−4, −1):

   • New coordinates: \((-1, 4)\)

2. Vertex M(0, −1):

   • New coordinates: \((-1, 0)\)

3. Vertex N(−4, −3):

   • New coordinates: \((-3, 4)\)

So, the image vertices after the rotation are:

• \(L′(−1, 4)\)
• \(M′(−1, 0)\)
• \(N′(−3, 4)\)

Now let's check the options provided:

1. L′(4, 1), M′(0, 1), N′(4, 3)
2. L′(−4, −1), M′(0, −1), N′(−4, −3)
3. L′(−1, 4), M′(−1, 0), N′(−3, 4)
4. L′(1, −4), M′(1, 0), N′(3, −4)

The correct choice is: L′(−1, 4), M′(−1, 0), N′(−3, 4), which corresponds to option 3.