A point is in Quadrant 3 and on the unit circle. If its x-coordinate is -4/5, what is the y-coordinate of the point?

Question

A point is in Quadrant 3 and on the unit circle. If its x-coordinate is -4/5, what is the y-coordinate of the point?

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Mộc Miên 4 years 2021-08-07T05:45:47+00:00 1 Answers 124 views 0

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  1. Nho
    0
    2021-08-07T05:47:37+00:00
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    Answer:

    The y-coordinate of the point is -3/5

    Step-by-step explanation:

    Here, we want to get the y-coordinate of the point

    when we talk of the unit circle, we mean a circle that has its radius equal to just 1 unit

    Now, on the third quadrant, we have the x axis value as negative, and also the y axis value as negative

    In the unit circle, the Pythagoras’ theorem works for all quadrants; with the radius representing the hypotenuse of the right triangle, the x and y coordinates value represents the other sides of the triangle

    Mathematically, from the theorem;

    the square of the hypotenuse (radius of the unit circle) equals the sum of the squares of the two other sides

    Thus, we have it that;

    1^2 = (-4/5)^2 + y^2

    1 = 16/25 + y^2

    y^2 = 1 – 16/25

    y^2 = 9/25

    y = √(9/25)

    y = +3/5 or -3/5

    But since the y-coordinate value is supposed to be negative, we have to choose y = -3/5 as our answer (for the third quadrant)

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