Answers: 1.) To translate a point, left and right affect the x-values, up and down affect the y-values. Here, 3 units left means subtract 3 from the x-value, and 5 units up means add 5 to the y-value. As a function this would be (x,y)-> (x-3, y+5), and for A(2, -3), we end up with (2-3, -3+5) which is A'(-1, 2).
2.) The translation (x,y)->(x+4, y-6) or 4 units right, 6 units down would map B to the origin.
3.) First: (-5+2, 2+4) which is (-3, 6) and then you take 1/3 of each coordinate, which gives us (1/3•-3, 1/3•6) which is (-1, 2).
4.) We have to remember length on the coordinate plane needs the pythagorean theorem. If you plot both points (0,0) and (6, 8), and make the right triangle between them, we would have legs of 6 (x-distance) and 8 (y-distance), which used in the Pythagorean Thm give us 6^2+8^2=c^2, which gives us 36+64=c^2, or 100=c^2, and then taking the square root of each side, we get c=10, so the distance is 10.
We then practiced in SpringBoard p. 244-245: 15-19.
HW#4: p. 247 ALL