An equilateral triangle on the coordinate plane has vertices at (–1, 2) and (4, 2). What are the possible coordinates of the third vertex rounded to the nearest tenth?

Question

1. 
   
2. A.
3. (–1.5, 6.3)
4. 
   
5. B.
6. (1.5, –2.3)
7. 
   
8. C.
9. (1.5, 6.3)
10. 
    
11. D.
12. (1.5, 6.6)
13. 
    
14. E.
15. (1.5, –6.6)
16. 
    
17. F.
18. (1.5, –6.3)

Answer 1

Start by plotting the 2 given points on graph paper. We see that one side of the triangle is on the line Y=2, and extends from X= -1 to +4

We now know that all three sides of the triangle are 5 units long.

There are only 2 possible locations for the 3rd vertex---The x value will be 1/2 the distance between -1 and +4 .....namely at x = +1.5. Draw a vertical line for this.

next, sketch in the 2 missing sides---for each option.

The last step is to calculate the height of the triangle. Get this in one of 2 ways:

pythagorean theorem---you know the hypotenuse (5 units) and one side 5/2 units

trig---each angle of an equilateral triangle is 60 deg. so the height is 5 * sin(60)

Once you have the height, the y coordinate of the 2 possible vertices is 2 + h, and 2 - h