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?

Answer 1

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

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)