b To reflect a point across the x-axis, we have to bring it over the x-axis so that the segments between the x-axis and the original point are congruent with the segments between the x-axis and the reflected point. These segments have to be perpendicular to the x-axis as well.
Examining the diagram, we can identify the coordinates of B' as (- 1,6). To determine the function that changes the coordinates of â–³ ABC to â–³ A'B'C', we should compare the vertices of â–³ ABC with the corresponding vertices of â–³ A'B'C'.
ccc
△ ABC & → & △ A'B'C'
A(- 3, - 4) & → & A'(- 3, 4)
B(- 1, - 6) & → & B'(- 1, 6)
C(- 5, - 8) & → & C'(- 5, 8)
Examining the corresponding vertices, we see that we have to change the sign of the y-coordinate to reflect â–³ ABC across the x-axis, forming â–³ A'B'C'.
rcl
(x,y) & → & (x,- y)
c To rotate a point clockwise about the origin, we first have to draw a segment from the point to the origin. Using a protractor, we measure a 90^(∘) angle clockwise and then draw a second segment of the same length as the first. At the end of this segment we find the rotated point. Let's do this with A'.
If we repeat this procedure for B' and C' we can draw the rotated triangle.
Examining the diagram, we see that the coordinates of C'' is (8,5).
d To perform the translation we have to move each of the vertices by 5 units in the positive horizontal direction and 1 unit in the positive vertical direction.
Examining the diagram, we see that the new coordinates of A is (2,- 4).
