Answer:
The possible coordinates of point A are [tex]A_{1} (x,y) = (-8, 14)[/tex] and [tex]A_{2} (x,y) = (-8, -10)[/tex], respectively.
Step-by-step explanation:
From Analytical Geometry, we have the Equation of the Distance of a Line Segment between two points:
[tex]l_{AB} = \sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2}}[/tex] (1)
Where:
[tex]l_{AB}[/tex] - Length of the line segment AB.
[tex]x_{A}, x_{B}[/tex] - x-coordinates of points A and B.
[tex]y_{A}, y_{B}[/tex] - y-coordinates of points A and B.
If we know that [tex]l_{AB} = 15[/tex], [tex]x_{A} = -8[/tex], [tex]x_{B} = 1[/tex] and [tex]y_{B} = 2[/tex], then the possible coordinates of point A is:
[tex]\sqrt{(1+8)^{2}+(2-y_{A})^{2}} = 15[/tex]
[tex]81 + (2-y_{A})^{2} = 225[/tex]
[tex](2-y_{A})^{2} = 144[/tex]
[tex]2-y_{A} = \pm 12[/tex]
There are two possible solutions:
1) [tex]2-y_{A} = -12[/tex]
[tex]y_{A} = 14[/tex]
2) [tex]2 - y_{A} = 12[/tex]
[tex]y_{A} = -10[/tex]
The possible coordinates of point A are [tex]A_{1} (x,y) = (-8, 14)[/tex] and [tex]A_{2} (x,y) = (-8, -10)[/tex], respectively.
