Option E (23,13)
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Now,
Verify each case
case A) (-9,-12)
Determine the distance and then compare with the given length of 17 units
R(6,-4)
[tex]d=\sqrt{(-4+12)^{2}+(6+9)^{2}}[/tex]
[tex]d=\sqrt{289}[/tex]
d = 17 units
therefore,
The given point can be the coordinates of S because the length RS is 17 units
case B) (23,-4)
Determine the distance and then compare with the given length of 17 units
R(6,-4)
[tex]d=\sqrt{(-4+4)^{2}+(6-23)^{2}}[/tex]
[tex]d=\sqrt{289}[/tex]
d=17 units
therefore
The given point can be the coordinates of S because the length RS is 17 units
case C) (6,13)
Determine the distance and then compare with the given length of 17 units
R(6,-4)
[tex]d=\sqrt{(-4-13)^{2}+(6-6)^{2}}[/tex]
[tex]d=\sqrt{289}[/tex]
d=17 units
therefore
The given point can be the coordinates of S because the length RS is 17 units
case D) (14,11)
Determine the distance and then compare with the given length of 17 units
R(6,-4)
[tex]d=\sqrt{(-4-11)^{2}+(6-14)^{2}}[/tex]
[tex]d=\sqrt{289}[/tex]
d=17 units
therefore
The given point can be the coordinates of S because the length RS is 17 units
case E) (23,13)
Determine the distance and then compare with the given length of 17 units
R(6,-4)
[tex]d=\sqrt{(-4-13)^{2}+(6-23)^{2}}[/tex]
[tex]d=\sqrt{578}[/tex]
d= 24.04 units
therefore
The given point cannot be the coordinates of S because the length RS is not 17 units
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