Question

point b has coordinates (5,1). the x - coordinate of point a is - 7. the distance between point a and point b is 15 units. what are the possible coordinates of point a? the possible coordinates of point a are \boxed{}. (type an ordered pair. use a comma to separate answers as needed.)

Explanation:

Step1: Recall distance formula for vertical/horizontal? Wait, x-coordinate of A is -7, B is (5,1). So A is (-7, y), B is (5,1). Distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Here, $d = 15$, $x_1 = -7$, $x_2 = 5$, $y_1 = y$, $y_2 = 1$. So:

$15 = \sqrt{(5 - (-7))^2 + (1 - y)^2}$

Step2: Simplify inside the square root:

$(5 + 7) = 12$, so $15 = \sqrt{12^2 + (1 - y)^2}$

Step3: Square both sides:

$15^2 = 12^2 + (1 - y)^2$ → $225 = 144 + (1 - y)^2$

Step4: Subtract 144:

$225 - 144 = (1 - y)^2$ → $81 = (1 - y)^2$

Step5: Take square roots:

$1 - y = \pm 9$

Step6: Solve for y:

Case 1: $1 - y = 9$ → $-y = 8$ → $y = -8$
Case 2: $1 - y = -9$ → $-y = -10$ → $y = 10$
So possible coordinates: (-7, -8) or (-7, 10)

Answer:

(-7, -8), (-7, 10)