Question

a transformation is the image. ( is read as \prime\) is the pre - image and can change the position or size of a figure. when a transformation preserves the size and shape of figure, all sides and angles of the pre - image and image are congruent. examples of rigid motions: to vertically and/or horizontally slide a figure. coordinate notation: (x,y)→(x + h,y + k) h represents the horizontal shift k represents the vertical shift. graph and label each figure and its image under the given translation. identify the coordinates of the image. 1. rectangle qrst with vertices q(-6,-1),r(-3,1),s(1,-5), and t(-2,-7): (x,y)→(x + 5,y + 7) 2. triangle cde with vertices c(2,-1), d(7,-4), and e(4,-6): (x,y)→(x - 3,y + 8) q: (-1,6) s: (6,2) c: e: r: (2,8) t: (3,0) d:

Explanation:

Step1: For rectangle QRST with translation $(x,y)\to(x + 5,y + 7)$

For point $Q(-6,-1)$:
$x=-6,y = - 1$
New $x=-6 + 5=-1$, new $y=-1 + 7=6$ so $Q'(-1,6)$
For point $R(-3,1)$:
$x=-3,y = 1$
New $x=-3+5 = 2$, new $y=1 + 7=8$ so $R'(2,8)$
For point $S(1,-5)$:
$x = 1,y=-5$
New $x=1 + 5=6$, new $y=-5 + 7=2$ so $S'(6,2)$
For point $T(-2,-7)$:
$x=-2,y=-7$
New $x=-2 + 5=3$, new $y=-7 + 7=0$ so $T'(3,0)$

Step2: For triangle CDE with translation $(x,y)\to(x - 3,y + 8)$

For point $C(2,-1)$:
$x = 2,y=-1$
New $x=2-3=-1$, new $y=-1 + 8=7$ so $C'(-1,7)$
For point $D(7,-4)$:
$x = 7,y=-4$
New $x=7-3 = 4$, new $y=-4 + 8=4$ so $D'(4,4)$
For point $E(4,-6)$:
$x = 4,y=-6$
New $x=4-3=1$, new $y=-6 + 8=2$ so $E'(1,2)$

Answer:

1. $Q'(-1,6),R'(2,8),S'(6,2),T'(3,0)$
2. $C'(-1,7),D'(4,4),E'(1,2)$