Question

AB is reflected to form A'B'. The coordinates of point A are (0,2) and the coordinates of point B are (2,5). Which reflection results in the transformation of AB to A'B'?

Answer 1

Answer:

The correct answer is 3 x + 2 y = 10.

Step-by-step explanation:

Let us find the midpoint of the given two points (0,2) and (2,5).

The midpoint is given by $(\frac{2+0}{2} , \frac{5+2}{2} )= ( 1, \frac{7}{2} )$.

Let us find the equation of the line passing through the two given points (0,2) and (2,5). We use the formula $y - \beta = m ( x - \alpha )$ where m is the slope of the line and ($\alpha ,\beta$) is any point on the line.

Thus the required line is given by $2 y - 3 x - 4 = 0.$

The line perpendicular to this line would give us the line of reflection.

So the equation of the line of reflection is $-3x-2y+k=0.$ ( A line perpendicular to $ax+by+c=0$ is given by $bx-ay+d=0$)

The midpoint ($1, \frac{7}{2}$) should pass through the line of reflection.

Thus this gives the value of k = 10.

So the required line of reflection is given by $3x+2y-10=0.$

Answer 2

Answer:

AB is reflected across the y axis to form A'B'

Step-by-step explanation:

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