Question

1 there are two points a (1, 3) and b (-4, 2) on the coordinate plane. answer the questions below.
(1) plot on the coordinate plane point c, given that point a was moved to the right 4 units. find the coordinates of point c.
(ans.) (_, _)
(2) plot on the coordinate plane point d, given that point a was moved to the left 3 units. find the coordinates of point d.
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(3) plot on the coordinate plane point e, given that point b was moved up 3 units. find the coordinates of point e.
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(4) plot on the coordinate plane point f, given that point b was moved down 2 units. find the coordinates of point f.
(ans.) (_, _)
(5) find the coordinates of a point, given point b was moved up 6 units.
(ans.) (_, _)
(6) find the coordinates of a point, given point b was moved down 6 units.
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(7) find the coordinates of a point, given point a was moved up 3 units.
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(8) find the coordinates of a point, given point a was moved to 2 units right and 3 units up.
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(9) find the coordinates of a point, given point a was moved to 6 units right and 6 units up.
(ans.) (_, _)

Explanation:

Step1: Right move: add to x-coordinate

Point A: $(1, 3)$. New $x=1+4=5$, $y=3$.

Step2: Left move: subtract from x-coordinate

Point A: $(1, 3)$. New $x=1-3=-2$, $y=3$.

Step3: Up move: add to y-coordinate

Point B: $(-4, 2)$. New $y=2+3=5$, $x=-4$.

Step4: Down move: subtract from y-coordinate

Point B: $(-4, 2)$. New $y=2-2=0$, $x=-4$.

Step5: Up 6 units: add 6 to y-coordinate

Point B: $(-4, 2)$. New $y=2+6=8$, $x=-4$.

Step6: Down 6 units: subtract 6 from y-coordinate

Point B: $(-4, 2)$. New $y=2-6=-4$, $x=-4$.

Step7: Up 3 units: add 3 to y-coordinate

Point A: $(1, 3)$. New $y=3+3=6$, $x=1$.

Step8: Right 2, up 3: adjust x and y

Point A: $(1, 3)$. New $x=1+2=3$, $y=3+3=6$.

Step9: Right 6, up 6: adjust x and y

Point A: $(1, 3)$. New $x=1+6=7$, $y=3+6=9$.

Answer:

1. $(5, 3)$
2. $(-2, 3)$
3. $(-4, 5)$
4. $(-4, 0)$
5. $(-4, 8)$
6. $(-4, -4)$
7. $(1, 6)$
8. $(3, 6)$
9. $(7, 9)$