Question

Transformation MATHS anyone pls help me fond a solution to this ques

Answer 1

Answer:   (-h, -g)

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Explanation:

Transformation V reflects over the line y = 0, which is the x axis. All points on the x axis have a y coordinate of zero. Examples are (1,0) and (2,0).

To reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. Example: The point (1,5) moves to (1,-5).

In general the rule is $(x,y) \to (x,-y)$

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Transformation W rotates the point 90 degrees clockwise around the origin (0,0). The rotation rule is $(x,y) \to (y,-x)$.

For example, the point (1,7) rotates to (7,-1) when doing a 90 degree clockwise rotation around the origin. We move from the northeast quadrant to the southeast quadrant.

As you can see, we swap the x and y coordinates. Then we do a sign flip on the new y coordinate.

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Transformation X combines the two previous transformations. We do V first then W next. The order is important (see the next section as to why).

We're given the point (g,h) where we don't know g nor h.

The x axis reflection rule has us get to (g, -h) because we simply flip the y coordinate from positive to negative, or vice versa.

Then applying transformation W has us get to (-h, -g) as the final answer.

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As stated earllier, the order of the transformations is important. Let's say we did W first and then V next.

1. Apply transformation W to go from (g,h) to (h,-g)
2. Apply transformation V to go from (h,-g) to (h,g)

The point (h,g) is different from (-h, -g) showing that the order does affect where the final point ends up.

However, some transformations can be composited together without worrying about the order. An example could be having a translation followed by another different translation.