Which of the following points lie on the $y$-axis?
$A(1,1), B(1,0), C(0,1), D(0,0), E(0,-1)$
$F(-1,0), G(0,5), H(-7,0), I(3,3)$
$A(1,1), B(1,0), C(0,1), D(0,0), E(0,-1)$
$F(-1,0), G(0,5), H(-7,0), I(3,3)$
(C, D, E, G) We know that if a point lies on the $y$-axis,its abscissa ($x$-coordinate) must be $0$. Therefore,the coordinates of such a point are of the form $(0, y)$.
Checking the given points:
$A(1,1)$: $x=1 \neq 0$
$B(1,0)$: $x=1 \neq 0$
$C(0,1)$: $x=0$ (Lies on $y$-axis)
$D(0,0)$: $x=0$ (Lies on $y$-axis)
$E(0,-1)$: $x=0$ (Lies on $y$-axis)
$F(-1,0)$: $x=-1 \neq 0$
$G(0,5)$: $x=0$ (Lies on $y$-axis)
$H(-7,0)$: $x=-7 \neq 0$
$I(3,3)$: $x=3 \neq 0$
Thus,the points that lie on the $y$-axis are $C(0,1), D(0,0), E(0,-1),$ and $G(0,5)$.
Checking the given points:
$A(1,1)$: $x=1 \neq 0$
$B(1,0)$: $x=1 \neq 0$
$C(0,1)$: $x=0$ (Lies on $y$-axis)
$D(0,0)$: $x=0$ (Lies on $y$-axis)
$E(0,-1)$: $x=0$ (Lies on $y$-axis)
$F(-1,0)$: $x=-1 \neq 0$
$G(0,5)$: $x=0$ (Lies on $y$-axis)
$H(-7,0)$: $x=-7 \neq 0$
$I(3,3)$: $x=3 \neq 0$
Thus,the points that lie on the $y$-axis are $C(0,1), D(0,0), E(0,-1),$ and $G(0,5)$.
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