Question

RS has an endpoint at R(6,- 4) and length 17. Which of the following cannot be the coordinates of S?

Answer 1

Answer:

Option E (23,13)

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Verify each case

case A) (-9,-12)

Determine the distance and then compare with the given length of 17 units

R(6,-4)

$d=\sqrt{(-4+12)^{2}+(6+9)^{2}}$

$d=\sqrt{289}$

$d=17\ units$

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)

$d=\sqrt{(-4+4)^{2}+(6-23)^{2}}$

$d=\sqrt{289}$

$d=17\ units$

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)

$d=\sqrt{(-4-13)^{2}+(6-6)^{2}}$

$d=\sqrt{289}$

$d=17\ units$

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)

$d=\sqrt{(-4-11)^{2}+(6-14)^{2}}$

$d=\sqrt{289}$

$d=17\ units$

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)

$d=\sqrt{(-4-13)^{2}+(6-23)^{2}}$

$d=\sqrt{578}$

$d=24.04\ units$

therefore

The given point cannot be the coordinates of S because the length RS is not 17 units