Question

coordinate plane

find the unknown coordinate for each reflection.

figure abcde is reflected across the y - axis to form figure abcde.
1 a(___, 6)
2 b(___, 5)
3 c(-4, ___)
4 d(-2, ___)
5 e(___, 4)
figure fghij is reflected across the x - axis to form figure fghij.
6 f(___, 2)
7 g(___, 2)
8 h(-1, ___)
9 i(-3, ___)
10 j(-5, ___)

Explanation:

Step1: Recall reflection rule across y - axis

When a point $(x,y)$ is reflected across the $y$-axis, the new point is $(-x,y)$.

Step2: Find coordinates for reflection of ABCDE across y - axis

For point $A$, assume its original $x$-coordinate is $3$ (from the graph), so $A'(-3,6)$. For $B$, assume original $x = 4$, so $B'(-4,5)$. For $C$, original $x = 4$, so $C'(-4,2)$. For $D$, original $x = 2$, so $D'(-2,2)$. For $E$, original $x = 1$, so $E'(-1,4)$.

Step3: Recall reflection rule across x - axis

When a point $(x,y)$ is reflected across the $x$-axis, the new point is $(x,-y)$.

Step4: Find coordinates for reflection of FGHIJ across x - axis

For point $F$, assume original $x=-5$, so $F'(-5,2)$. For $G$, original $x = - 3$, so $G'(-3,2)$. For $H$, original $y=-4$, so $H'(-1,4)$. For $I$, original $y=-6$, so $I'(-3,6)$. For $J$, original $y=-4$, so $J'(-5,4)$.

Answer:

1. $-3$
2. $-4$
3. $2$
4. $2$
5. $-1$
6. $-5$
7. $-3$
8. $4$
9. $6$
10. $4$