Question

the coordinates of a polygon are (2,3), (4,7), (8,5), and (7,2). if the polygon rotates 90° clockwise about the origin, in which quadrant will the transformation lie? what are the new coordinates? a quad ii, (-2,3), (-4,7), (-8,5), and (-7,2) b quad iv, (3,-2), (7,-4), (5,-8), and (2,-7) c quad iii, (-2,-3), (-4,-7), (-8,-5), and (-7,-2) d quad iii, (-3,-2), (-7,-4), (-5,-8), and (2,-7)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) rotates \(90^{\circ}\) clockwise about the origin, the new coordinates become \((y,-x)\).

Step2: Apply the rule to each point

• For the point \((2,3)\): \(x = 2,y = 3\). After rotation, the new coordinates are \((3,-2)\).
• For the point \((4,7)\): \(x = 4,y = 7\). After rotation, the new coordinates are \((7,-4)\).
• For the point \((8,5)\): \(x = 8,y = 5\). After rotation, the new coordinates are \((5,-8)\).
• For the point \((7,2)\): \(x = 7,y = 2\). After rotation, the new coordinates are \((2,-7)\).

Step3: Determine the quadrant

In the coordinate system, points with positive \(x\)-coordinate and negative \(y\)-coordinate lie in Quadrant IV.

Answer:

B. Quad IV, \((3, - 2)\), \((7, - 4)\), \((5, - 8)\), and \((2, - 7)\)