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kenny6666 [7]
3 years ago
9

PLEASE SOMEONE HELP ILL GIVE BRAINLIEST!

Mathematics
1 answer:
grin007 [14]3 years ago
5 0

Answer:

Part A

The rotation of the point (x, y) 180° about the origin gives the point (-x, -y)

Therefore, we have the points, ΔLMN, L(1, 1), and M(2, 2), and N(3, 3)

The coordinates of the vertices of the image, ΔL'M'N' are L'(-1, -1), and M'(-2, -2), and N'(-3, -3)

Please find attached the graph of triangle ΔLMN and ΔL'M'N'

Part B

The lines drawn through L and L' and through M and M' are colinear

Part C

A line is defined by two points, such as <em>L </em>and <em>M.</em> Rotation of a line through 180° about the origin will give an image location on the same path as the extension of the original line.

The third point, <em>N</em>, however, defines a plane, and the rotation of a plane by 180° will give an image which is turned upside down with regards to the preimage

Therefore, a trough in the preimage becomes a peak in the image and the lines drawn through N and N' crosses the colinear lines drawn throgh M and M' and L and L'

Step-by-step explanation:

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Answer:

  a) 5 cm

  b) 8 cm

  c) 9 m

Step-by-step explanation:

It can be worthwhile to work the last attachment (a) first, since these are all variations of the same triangle.

The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse.

<u>Problem 6a</u>:

  3² +4² = x² . . . . fill in the given numbers; all measures in cm

  9 + 16 = x² . . . . simplify exponents

  25 = x² . . . . . . . simplify sum

  x = √25 = 5 . . . take the square root.

  x = 5 cm . . . . . . apply units

__

Note that this triangle is a 3-4-5 right triangle. That is a set of side lengths (ratios) that is useful to remember. In this problem set, you see it again immediately.

__

<u>Problem 6b</u>:

Shortest-to-longest, the side ratios of the given triangle are ...

  6 : x : 10

For some x', this is ...

  3 : x' : 5 . . . . . . . . . . . . . matches a 3-4-5 triangle with x' = 4

The scale factor is 6/3 = 10/5 = 2, so we have ...

  x = 2·x' = 2·4 = 8

  x = 8 cm . . . . . with units

__

<u>Problem 6c</u>:

The side ratios are ...

  x : 12 : 15  which reduces to  x' : 4 : 5

This matches a 3-4-5 triangle with x' = 3, and a scale factor of 12/4 = 15/5 = 3.

Then ...

  x = 3·x' = 3·3 = 9

  x = 9 m . . . . . with units

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