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 - 7, - 8 - 7,10. (type an ordered pair. use a comma)
× thats incorrect.
ordered pairs must be separated by a comma.
ok
×

Explanation:

Step1: Recall the distance formula for vertical or horizontal lines. Since the x - coordinate of A is - 7 and B is (5,1), we consider the vertical distance? Wait, no, the x - coordinates: the distance between x - coordinates of A and B is |x_A - x_B|=|-7 - 5| = 12. But the total distance is 15. So we use the Pythagorean theorem? Wait, no, maybe the points are vertical? Wait, no, the y - coordinate of B is 1. Let the coordinates of A be (-7,y). The distance between A(-7,y) and B(5,1) is given by the distance formula: $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. We know d = 15, $x_1=-7,x_2 = 5,y_2 = 1,y_1=y$. So $15=\sqrt{(5 - (-7))^2+(1 - y)^2}$.

Step2: Simplify the equation. First, calculate $(5 - (-7))^2=(12)^2 = 144$. So the equation becomes $15=\sqrt{144+(1 - y)^2}$. Square both sides: $15^2=144+(1 - y)^2$. So $225 = 144+(1 - y)^2$. Subtract 144 from both sides: $(1 - y)^2=225 - 144 = 81$.

Step3: Solve for y. Take square roots: $1 - y=\pm9$. Case 1: $1 - y = 9\Rightarrow y=1 - 9=-8$. Case 2: $1 - y=-9\Rightarrow y=1+9 = 10$. So the coordinates of A are (-7,-8) or (-7,10). The error in the previous answer was the formatting of the ordered pair. The correct ordered pairs should be (-7, - 8) and (-7,10) (but the question says "the possible coordinates of point A" (maybe one? Wait, the problem says "the possible coordinates" - maybe we consider the two cases. But the user's previous answer was formatted incorrectly. The correct ordered pair should be in the form (x,y). So for A, x is - 7, y is - 8 or 10. So possible coordinates are (-7,-8) or (-7,10).

Answer:

(-7, - 8) or (-7, 10) (if we take one, either (-7, - 8) or (-7, 10); but since the distance is 15, both are possible. The previous answer had a formatting error, the ordered pair should be separated by a comma between x and y, like (-7, - 8) or (-7, 10))