Find the distance between J (-5, 4) and K (3, 2)

Mathematics

1 answer:

ddd [48]2 years ago

8 0

Answer:

$distance = \sqrt{ {(3 - ( - 5))}^{2} + {(2 - 4)}^{2} } \\ = \sqrt{ {8 {}^{2} + {( - 2)}^{2} } } \\ = \sqrt{68} \\ = 8.25 \: units$

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What is the image of point (4, 5) after a counterclockwise rotation of 270º about the origin?

andriy [413]

A counterclockwise rotation of 270º about the origin is equivalent to a clockwise rotation of 90º about the origin.

Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.

A clockwise rotation of 90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, a counterclockwise rotation of 270º about the origin which is equivalent to a clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)

Therefore, a counterclockwise rotation of 270º about the origin of the point (4, 5) will result in an image with the coordinate of (5, -4) (option C)

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3 years ago

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nikdorinn [45]

Answer:

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Convert 3.92 into mixed fraction in simplest form

anygoal [31]

$3.92=3+0.92=3+\frac{92}{100}=3+\frac{92:4}{100:4}=3+\frac{23}{25}=\boxed{3\frac{23}{25}}$