Question

△elm is rotated $-90^{circ}$ about the origin. draw the image of this rotation.

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of \( E \), \( L \), \( M \) from the graph. Let's assume:

• \( E=(0, 3) \) (on y - axis, y = 3)
• \( L=(3, - 2) \) (x = 3, y=-2)
• \( M=(-2, - 2) \) (x=-2, y = - 2)

Step2: Apply rotation rule for \(-90^{\circ}\) (or \(270^{\circ}\) clockwise) about origin

The rule for rotating a point \((x,y)\) by \(-90^{\circ}\) about the origin is \((x,y)\to(y, - x)\).

• For \( E=(0,3) \):

Using the rule \((x,y)\to(y, - x)\), we get \( E'=(3,0) \) (since \( x = 0,y = 3\), so \( y = 3,-x=0\))

• For \( L=(3,-2) \):

Using the rule \((x,y)\to(y, - x)\), we get \( L'=(-2,-3) \) (since \( x = 3,y=-2\), so \( y=-2,-x = - 3\))

• For \( M=(-2,-2) \):

Using the rule \((x,y)\to(y, - x)\), we get \( M'=(-2,2) \) (since \( x=-2,y = - 2\), so \( y=-2,-x = 2\))

Step3: Plot the new points and draw the triangle

Plot the points \( E'=(3,0) \), \( L'=(-2,-3) \), \( M'=(-2,2) \) on the coordinate plane and connect them to form the image of \(\triangle ELM\) after rotation.

Answer:

To draw the image of \(\triangle ELM\) after a \(-90^{\circ}\) rotation about the origin:

1. Find the coordinates of the vertices of \(\triangle ELM\) (e.g., \( E=(0,3) \), \( L=(3,-2) \), \( M=(-2,-2) \) from the graph).
2. Apply the rotation rule \((x,y)\to(y, - x)\) to each vertex:

• \( E(0,3)\to E'(3,0) \)
• \( L(3,-2)\to L'(-2,-3) \)
• \( M(-2,-2)\to M'(-2,2) \)

1. Plot the points \( E' \), \( L' \), \( M' \) and connect them to form the rotated triangle.