Question

question 6 5 pts which of the following points is the reflection of (4,-3) over the x - axis? (4,3) (-4,3) (-4,-3) (4,-3) if a point (a,b) is reflected over the y - axis, what are the coordinates of the image? (b,a) (-a,-b) (-a,b) (a,-b)

Explanation:

Step1: Recall reflection rule over x - axis

When a point $(x,y)$ is reflected over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign. The rule is $(x,y)\to(x, - y)$.

Step2: Apply the rule to the point $(4,-3)$

For the point $(4,-3)$, with $x = 4$ and $y=-3$, after reflection over the x - axis, the new y - coordinate is $-(-3)=3$ and the x - coordinate remains 4. So the reflected point is $(4,3)$.

Step1: Recall reflection rule over y - axis

When a point $(x,y)$ is reflected over the y - axis, the y - coordinate remains the same and the x - coordinate changes its sign. The rule is $(x,y)\to(-x,y)$.

Step2: Apply the rule to the point $(a,b)$

For the point $(a,b)$, with $x = a$ and $y = b$, after reflection over the y - axis, the new x - coordinate is $-a$ and the y - coordinate remains $b$. So the reflected point is $(-a,b)$.

Answer:

$(4,3)$