5. Justify the last two steps of the proof.
1 answer:
Answer:
ST & TS are congruent
RST and UTS are congruent
Step-by-step explanation:
The question is not properly presented; however, I've added an attachment to give a clear picture of the question.
Required
State the property that justifies:
Triangles
From the question, we have that:
In plane geometry, the length of ST is still the same as the length of TS.
This implies that:
because ST is congruent to TS
Moving further to determine the relationship between triangles
Comparing both triangles:
They have a similar side ST and TS because
And we also have that:
So, we can conclude that: because they are congruent
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9514 1404 393
Answer:
(a) vertical compression by a factor of 1/3
Step-by-step explanation:
We can see that g(x) = 1/3f(x). Multiplying a function by a constant scales the graph vertically by that factor. When the magnitude of the factor is more than 1, we say the graph is "stretched." When it is less than 1, we say the graph is "compressed" by that factor.
Here, the scale factor is 1/3, so the graph is "vertically compressed by a factor of 1/3."
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<em>Additional comment</em>
My <em>personal</em> preference is for compression to be described by the factor the graph is divided by. I would call g(x) a compression of f(x) by a factor of 3. Modern curriculum authors disagree, calling it compression by a factor of 1/3.
Be careful. Using the currently accepted language, a <em>stretch</em> is always by a number <em>larger than 1</em>, and a <em>compression</em> is always by a number <em>less than 1</em>. This rules out choices C and D simply on the basis of the language used.
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For many graphs, vertical scaling and horizontal scaling can be interchanged. We note that g(x) is wider than f(x), so could be stretched horizontally by some factor. That factor would be √3. The equation using a horizontal stretch factor would be g(x) = (x/√3)^2. Replacing x by x/k is a stretch by a factor of k in the horizontal direction.
