Answer:
The possible coordinates for R are contained in the following expression:
Explanation:
From statement we notice that line segment PQ is parallel to x-axis and by Geometry we know that an equilateral triangles have three side with equal length and three angles of 60°. In consequence, the height of the triangle is parallel to the y-axis and the possible coordinates for point R are contained in this equation:
(1)
Where:
,
- Coordinates of the midpoint of the line segment PQ.
- Side length of the line segment PQ.
The length of the line segment PQ is determined by the Pythagorean Theorem:
(2)
If we know that and
, then the length of the line segment PQ is:
And the coordinates of the midpoint are, respectively:
Lastly, the possible coordinates of vertex R are, respectively: