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3 years ago

Find the image of NPQ under the translation of (x,y) -> (x + 8, y + 1).

Mathematics

1 answer:

lina2011 [118]3 years ago

8 0

Answer:

The image triangle NPQ is triangle KLM

Step-by-step explanation:

The vertices of triangle NPQ are at:

N(-7,-6), P(-4,-3) an Q(-4,-6).

The rule for the translation is:

$(x,y)\to(x+8,y+1)$

This implies that:

$N(-7,-6)\to (-7+8,-6+1)=N'(1,-5)$

$P(-4,-3)\to (-4+8,-3+1)=P'(4,-2)$

$Q(-4,-6)\to (-4+8,-6+1)=Q'(4,-5)$

Therefore triangle N'P'Q' has vertices at N'(1,-5),P'(4,-2), and Q'(4,-5)

This coincides with K(1,-5),L(4,-2), and M(4,-5)

Hence the image triangle NPQ is triangle KLM

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The distance between the bottom of the lighthouse and the boat is 77.6m.

<h3>What is the distance between the bottom of the lighthouse and the boat?</h3>

The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The distance between the top of the lighthouse and boat would be the hypotenuse. The distance between the bottom of the lighthouse and the boat would be the base.

In order to determine the required distance, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where:
a = length
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125² = 98² + b²

b² = 125² - 98²

b = √(25² - 98² )

b = 77.6m

To learn more about Pythagoras theorem, please check: brainly.com/question/14580675

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2 years ago

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Assume we need to estimate the mean of a normally-distributed population with great accuracy. Specifically, for significance lev

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