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Math  /  Geometry

Question3. Write the coordinates of the vertices after a rotation of 90∘90^{\circ} counterclockwise around th origin. Then draw the rotated image. A

Studdy Solution

STEP 1

1. The rotation is 90∘90^\circ counterclockwise around the origin.
2. The original coordinates of the vertices are L(−5,−10)L(-5, -10), M(0,−10)M(0, -10), and N(−9,−6)N(-9, -6).

STEP 2

1. Recall the formula for rotating a point 90∘90^\circ counterclockwise around the origin.
2. Apply the rotation formula to each vertex.
3. Write the new coordinates of the vertices.
4. Draw the rotated image.

STEP 3

Recall the formula for rotating a point 90∘90^\circ counterclockwise around the origin:
If a point (x,y)(x, y) is rotated 90∘90^\circ counterclockwise, its new coordinates are (−y,x)(-y, x).

STEP 4

Apply the rotation formula to each vertex:
For L(−5,−10)L(-5, -10): New coordinates are (−(−10),−5)=(10,−5)(-(-10), -5) = (10, -5).
For M(0,−10)M(0, -10): New coordinates are (−(−10),0)=(10,0)(-(-10), 0) = (10, 0).
For N(−9,−6)N(-9, -6): New coordinates are (−(−6),−9)=(6,−9)(-(-6), -9) = (6, -9).

STEP 5

Write the new coordinates of the vertices:
- L′=(10,−5)L' = (10, -5) - M′=(10,0)M' = (10, 0) - N′=(6,−9)N' = (6, -9)

STEP 6

Draw the rotated image by plotting the new coordinates L′(10,−5)L'(10, -5), M′(10,0)M'(10, 0), and N′(6,−9)N'(6, -9) on the coordinate plane.
The new coordinates of the vertices after the rotation are: - L′(10,−5)L'(10, -5) - M′(10,0)M'(10, 0) - N′(6,−9)N'(6, -9)

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