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Masja [62]
2 years ago
10

How far apart are parallel lines m and n such that T0, -123(AXYZ) = (R, Rm) (AXYZ)?

Mathematics
1 answer:
Dmitry_Shevchenko [17]2 years ago
7 0

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>

<u />

Reason:

The given parameters are;

T_{}\Delta(XYZ) = (R_n \circ R_m) \Delta (XYZ)

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 T_{} 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;

(n - m) = \dfrac{-12}{2}  = -6

Which gives;

m - n = 6

The distance between the two lines = 6 units

Learn more about reflection about a line here;

brainly.com/question/15339549

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