a Multiplying the y-coordinate by - 1 is the same thing as reflecting the point in the x-axis.
B
b Note that it is the original triangle that we should transform.
A
a A''=(- 3,- 6)
B''=(- 5,- 4)
C''=(0,- 4)
B
b A''=(3,3)
B''=(1,1)
C''=(1,6)
Practice makes perfect
a Let's graph the triangle.
When multiplying all the y-coordinates by - 1 you change the sign of the y-coordinate, which effectively reflects the triangle in the x-axis.
Point
(x,y)
(x,y(- 1))
A
(3,3)
(3,- 3)
B
(1,1)
(1,- 1)
C
(6,1)
(6,- 1)
When we know the coordinates of the reflected triangle, we can draw it in the diagram.
Finally, we also want to translate it by 6 units in the negative horizontal direction and 3 units in the negative vertical direction.
Point
(x,y)
(x-6,y-3)
A'
(3,- 3)
(- 3,- 6)
B'
(1,- 1)
(- 5,- 4)
C'
(6,- 1)
(0,- 4)
Let's draw the translated triangle.
b To rotate a vertice by 90^(∘) counterclockwise about the origin, we draw segments from it to the origin. Next, we use a protractor to draw a second segment that is at a 90^(∘) angle counterclockwise to the first segment. To find the coordinates of the rotated vertice, we have to make the second segment the same length as the first.
If we repeat the procedure for the remaining two points, we can draw the rotated triangle.
To reflect a vertice across the y-axis, we draw segments from each vertice towards, and perpendicular to the y-axis.
By extending these segments to the opposite side of the y-axis and with the same length as the corresponding first segment, we have reflected each vertice across the y-axis.
Examining the diagram, we can name the coordinates of the reflected triangle.
A''&=(3,3)
B''&=(1,1)
C''&=(1,6)
