Answer:
Point A does not lie on the curve y = x²
Step-by-step explanation:
Given points:
[tex]\sf A: \left(\dfrac{3}{2}, \dfrac{9}{2}\right)[/tex]
[tex]\sf B: \left(-1,1 \right)[/tex]
[tex]\sf C: \left(4,16 \right)[/tex]
[tex]\sf D: \left(\dfrac{1}{2}, \dfrac{1}{4}\right)[/tex]
To determine if the given points lie on the curve y = x², simply substitute the x-value of each point into the equation and compare y-values.
Point A
[tex]\boxed{\begin{aligned}x=\dfrac{3}{2} \implies y&=\left(\dfrac{3}{2} \right)^2\\\\y&=\dfrac{3^2}{2^2}\\\\y&=\dfrac{9}{4}\end{aligned}}[/tex]
As 9/4 ≠ 9/2, point A does not lie on the curve.
Point B
[tex]\boxed{\begin{aligned}x= -1\implies y&=\left(-1 \right)^2\\y&=1\end{aligned}}[/tex]
As 1 = 1, point B does lie on the curve.
Point C
[tex]\boxed{\begin{aligned}x=4 \implies y&=\left( 4\right)^2\\y&=16\end{aligned}}[/tex]
As 16 = 16, point C does lie on the curve.
Point D
[tex]\boxed{\begin{aligned}x=\dfrac{1}{2} \implies y&=\left(\dfrac{1}{2} \right)^2\\\\y&=\dfrac{1^2}{2^2}\\\\y&=\dfrac{1}{4}\end{aligned}}[/tex]
As 1/4 = 1/4, point D does lie on the curve.
