Triangle FGH is graphed on the coordinate plane below.

Mathematics

1 answer:

frozen [14]3 years ago

8 0

Answer:

(x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)

Step-by-step explanation:

Let us revise the rotation about the origin

If point (x, y) rotated about the origin by angle 90° counterclockwise (or 270° clockwise), then its image is (-y, x) . The rule is (x, y) → (-y, x)

If point (x, y) rotated about the origin by angle 180° counterclockwise ( or 180° clockwise), then its image is (-x, -y) . The rule is (x, y) → (-x, -y)

If point (x, y) rotated about the origin by angle 270° counterclockwise (90° clockwise), then its image is (y, -x) . The rule is (x, y) → (y, -x)

Let us solve the question

∵ The vertices of triangle FGH are (-6, -8), (-2, -3), (-4, -2)

∵ The figure is rotated 180° using the origin as the center of rotation

→ By using the 2nd rule above

∴ The vertices of its image are (6, 8), (2, 3), (4, 2)

∴ The rule is (x, y) → (-x, -y)

The coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image do (x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)

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The data below are times (in seconds) recorded when statistics students participated in an experiment to test their ability to d

RoseWind [281]

Answer:

Mean = 58.25

Median = 57.5

Mode = 49

Step-by-step explanation:

We are given the following data set:

55, 51, 74, 61, 67, 60, 49, 49

Formula:

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{466}{8} = 58.25$

Sorted data:

49, 49, 51, 55, 60, 61, 67, 74

Mode is the entry with highest frequency.

49 appeared two times.

Mode = 49

Formula:

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$