Answer:
a. The coordinates of A can be either [tex](5,\, 10)[/tex] or [tex](5,\, -14)[/tex].
b. The coordinate of A would now be either [tex](5,\, 7)[/tex] or [tex](5,\, -11)[/tex].
Step-by-step explanation:
Given the horizontal distance [tex]\Delta x = |x_2 - x_1|[/tex] and vertical distance [tex]\Delta y = |y_2 - y_1|[/tex] between two points, the distance between them would be [tex]\sqrt{(\Delta x)^2 + (\Delta y)^2}[/tex].
The horizontal distance between point A and point B is [tex]|5 - (-4)| = 9[/tex].
The vertical distance between these two points is unknown. It can be find using the distance formula.
[tex]\sqrt{9^2 + (\Delta y)^2} = 15[/tex].
Square both sides:
[tex]9^2 + (\Delta y)^2 = 15^2[/tex].
[tex]\Delta y = \sqrt{15^2 - 9^2} = 12[/tex].
In other words, the vertical distance between A and B is [tex]12[/tex].
The horizontal distance between point A and point B is [tex]|5 - (-7)| = 12[/tex].
The vertical distance between these two points is unknown. It can be find using the distance formula.
[tex]\sqrt{12^2 + (\Delta y)^2} = 15[/tex].
Square both sides:
[tex]12^2 + (\Delta y)^2 = 15^2[/tex].
[tex]\Delta y = \sqrt{15^2 - 12^2} = 9[/tex].
In other words, the vertical distance between A and B is [tex]9[/tex].
