Question

Which of the following coordinates represent the reflection of A and B, where $\text{A}=(3,1)\text{and B}=(2,4)$ across the x-axis?

• A. $A^{\prime }=(-3,1),B^{\prime }=(2,-4)$
• B. $A^{\prime }=(-3,1),B^{\prime }=(-2,-4)$
• C. $A^{\prime }=(3,-1),B^{\prime }=(-2,4)$
• D. $A^{\prime }=(3,-1),B^{\prime }=(2,-4)$

Answer 1

The correct option is D $A^{\prime }=(3,-1),B^{\prime }=(2,-4)$


Distance of A from the x-axis in the upward direction $=1$
Distance of point A from the y-axis in right direction $=3$
Therefore, the coordinates of Point A: $(3,1)$

The reflected point A' along the x-axis will be in the fourth quadrant with coordinates (x, -y).
The coordinates of the reflecting point A’ along the x-axis
$=A^{\prime }(3,-1)$

Distance of point B from the x-axis in the upward direction $=4$
Distance of point B from the y-axis in the right direction $=2$
Therefore, the coordinates of Point B: $(2,4)$

The reflected point B' along the x-axis will be in the fourth quadrant with coordinates (x, -y).
The coordinates of the reflecting Point B' along the x-axis $=B^{\prime }(2,-4)$

Therefore the correction option is B.