Answer:
(-1.5, -3.5) and (-1.5, 2)
Step-by-step explanation:
The x-coordinates in increasing order are ...
-3, -1.5, 5
The distances between pairs of these coordinates are ...
-1.5 -(-3) = 1.5
5 -(-3) = 8
5 -(-1.5) = 6.5
Clearly, any pair with x = 5 is too far away from any pair with a different x-value.
<u>∆x = 1.5</u>
If the distance between pairs is 5.5, then the distance formula tells us the y-coordinate differences for pairs with x-coordinates of -3 and -1.5 must be ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
5.5 = √(1.5^2 +(y2 -y1)^2) . . . substitute known values
30.25 = 2.25 +(y2 -y1)^2 . . . . square both sides
√28 = (y2 -y1) . . . . . . . . . . . . . . subtract 2.25 and take the square root
This value is irrational. Clearly none of the y-coordinates is irrational, so there are no point pairs with x-coordinates -3 and -1.5 that are 5.5 units apart.
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<u>∆x = 0</u>
If the x-coordinates are the same, then the y-coordinates must differ by 5.5 in order for the points to be 5.5 units apart. The coordinates in order are ...
for x = -1.5, y = -3.5, 2, 2.5 . . . . . differences of 5.5, 6, 0.25
for x = 5, y = -3.5, 1.5 . . . . . . . difference of 5
The only pair we can find that is 5.5 units apart is ...
(-1.5, -3.5) and (-1.5, 2).
(length 
), so the half range is 
. The half range sine series would then be given by
