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A reflection about a line gives an image that is at an equal distance from the line but on the opposite (other) side of the line
The distance between the lines <em>m</em> and <em>n</em> is <u>6 units</u>
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Reason:
The given parameters are;
Let <em>Y</em> represent the top vertex of Δ(XYZ), and the coordinates of point <em>Y</em> is (3, 0) we have;
The coordinates of Y following is Y''(3, -12)
A reflection of <em>Y </em> across the line m, y = -9, gives the coordinates of the image at Y'(3, -18)
A reflection of the image Y'(3, -18) across the line n, y = -15, gives the image at Y''(3, -12)
The distance between lines <em>m</em>, and line <em>n</em>, is -9 - (-15) = 6
Generally, the difference between two lines of reflection, <em>n</em>, and <em>m</em>, following a composite reflection is 2×(n - m)
Given that the total transformation is -12, we have;
2×(n - m) = -12
Therefore;
Which gives;
m - n = 6
The distance between the two lines = 6 units
Learn more about reflection about a line here;