Question

The vertices of ΔABC are A(−3,4)​, B(−2,4)​, and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image Δ​A'B'C', find the coordinates of the vertex B​'.
The coordinates of B​' after a reflection across the line y= -2

Answer 1

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$.

How to calculate the coordinate of point by reflection

A point if reflected across the line $y = -2$ by means of the following formula:

$P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)]$ (1)

Where:

• $P(x,y)$ - Original point
• $x_{P}$ - x-Coordinate of point P
• $P'(x,y)$ - Resulting point

If we know that $P(x,y) = (-2,4)$ and $x_{P} = -2$, then the coordinates of the vertex is:

$P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)]$

$P'(x,y) = (-2, 4) +2\cdot (0, -6)$

$P'(x,y) = (-2, 4) + (0,-12)$

$P'(x,y) = (-2, -8)$

The coordinates of vertex B' is $P'(x,y) = (-2, -8)$. $\blacksquare$

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