The equation of Line of reflection is y + 2x =6
What is section formula?
When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.
Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P= [tex](\frac{(mx_2 + nx_1} {2} . \frac{mx_1 + nx_2}{2} )[/tex]
It is given that,
- A=(-3,2)
- A'=(5,6),
- B=(2,-3)
- and B'=(6,-1),
As, the mid point of vertices of figure to the corresponding vertices of reflected figure should lie on reflected line.
Since, Δ ABC is reflected to Δ A'B'C' through this line,
Let, Q be the mid point of line AA', using section formula
Coordinate of Q = [tex](\frac{(-3) + 5}{2} . \frac{6+2}{2} ) = (1. 4 )[/tex]
and R be the mid point of line BB', using section formula
Coordinate of R = [tex](\frac{2 + 6}{2} . \frac{-3-1}{2} ) = (4. -2 )[/tex]
As Q and R lies on the line of the reflection,
Thus, the equation of the line of reflection,
[tex](y-4)=\frac{-2-4} {4-1} (x-1)[/tex]
3(y-4) = -6 (x-1)
3y - 12= 6 - 6x
3y + 6x = 18
y + 2x =6
The reflected line can be drawn by finding the solution of y+ 2x =6.
Learn more Section Formula here:
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