Label the vertices of the quadrilateral A, B, C, D. Angle C is supplementary to the angle of measure 60 degrees, so its own measure is 120 degrees.
AD and BC are parallel, as are AB and CD, so ABCD is a parallelogram. This means angle A also has measure 120 degrees. The angle adjacent to the one with measure , part of angle A, then has measure
.
The three angles above the line through vertex A are supplementary, so we have
The two possible positions of point P are:
(3, -5) and (0.6, 5.8)
<h3>How to find the two possible positions of point P?</h3>
We know that point P lies on the line:
y = 4 - 3*x
And that the distance between P and the origin is √34, then if the coordinates of point P are (x, y), we have that:
Now, we can replace "y" in the distance equation by the linear equation, and also remove the square roots:
Now we can solve the quadratic equation for x:
The solutions are:
So the two solutions are:
x = (24 + 36)/20 = 3
x = (24 - 36)/20 = -0.6
To get the points, we need to evaluate y on these values:
y = 4 - 3*3 = -5 So we have P = (3, -5)
y = 4 - 3*(-0.6) = 2.2 So we have the point (0.6, 5.8)
There are the two possible positions of point P.
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