Question

The point (3,2) is reflected in the y-axis and then moved a distance of 5 units towards the negative side of the y-axis. The coordinates of the point thus obtained is:
a)(3,-3)
b) (-3,3)
c) (3,3)
d) (-3,-3)

Answer 1

Hint : We are given a point (3,2) and are given certain movements to be done with this point. The question asks us to find the final destination of this point after these treatments. So we have to use the formulas of the 2-d coordinate plane and obtain the result.
Formula used:
The midpoint of two point A(m,n) and B(o,p) is C $\left( {\dfrac{{m + o}}{2},\dfrac{{n + p}}{2}} \right)$

Complete step-by-step answer :
We are given a point (3,2) and it is reflected along the y-axis.
Any reflection along y-axis will always keep the y coordinate constant
Let the reflected point be (x,2).
The midpoint of (3,2) and (x,2) will lie on the y- axis.
As any point on y-axis will have x-coordinate zero so we have,
$\Rightarrow \dfrac{{3 + x}}{2} = 0 \Rightarrow x + 3 = 0 \Rightarrow x = - 3$
Thus, reflection of point (3,2) along y-axis gives the point (-3,2)
We are also given that this point is shifted 5 units along negative y- axis
As it is moved 5 units along the negative direction of y- axis so we will subtract 5 from the y-coordinate of this point. SO we have: $(-3,2-5)=(-3,-3)$
So, the correct answer is “Option D”.

Note : Reflection along y-axis keeps y-coordinate fixed while the reflection along x-axis keeps the x-coordinate fixed. The treatment of reflection for a point along the y-axis gives negative coordinate values to the x- coordinate. Similarly, the treatment of reflection for a point along x-axis gives a negative coordinate value to the y- coordinate.