Question

we can certainly have point reflections in the coordinate plane. the most common is a reflection across the origin (i.e. a 180° rotation about the origin).
exercise #3: triangle mno is graphed with vertices at m(1,4), n(4,6), and o(8,2).
(a) draw the image of △mno after a reflection across the origin. label its image △mno. show the mapping below.
(b) give a general rule for reflecting a point across the origin.
f:(x,y)→
n-gen math geometry - unit 2 - rigid motions and congruence - lesson 4(y11.11.24)
emathinstruction, red hook, ny 12571, © 2023

Explanation:

Step1: Find the coordinates of the reflected points

The rule for reflecting a point \((x,y)\) across the origin is \((x,y)\to(-x,-y)\).
For point \(M(1,4)\), after reflection \(M'(- 1,-4)\).
For point \(N(4,6)\), after reflection \(N'(-4,-6)\).
For point \(O(8,2)\), after reflection \(O'(-8,-2)\).

Step2: Map the triangle

Plot the points \(M'(-1,-4)\), \(N'(-4,-6)\) and \(O'(-8,-2)\) on the coordinate plane and connect them to form \(\triangle M'N'O'\).

Answer:

(a) After reflection, \(M(1,4)\to M'(-1,-4)\), \(N(4,6)\to N'(-4,-6)\), \(O(8,2)\to O'(-8,-2)\). Plot these points to get \(\triangle M'N'O'\).
(b) The general rule for reflecting a point across the origin is \(f:(x,y)\to(-x,-y)\)