Sagot :
Answer:
The possible coordinates of point A are (-8,-4) or (-8,6)
Step-by-step explanation:
The distance between two points is given by the formula
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]
For point A [tex](x_{1} , y_{1})[/tex]; [tex]x_{1}= -8[/tex] and [tex]y_{1}[/tex] is unknown
For point B [tex](x_{2} , y_{2})[/tex]; (4,1) i.e [tex]x_{2}=4[/tex] and [tex]y_{2}=1[/tex]
and d = 13
Putting the values into the equation,
[tex]13= \sqrt{[(4-(-8)]^{2} + (1-y_{1})^{2} }\\13= \sqrt{[(4+8)]^{2} + (1-y_{1})^{2} }\\13= \sqrt{12^{2} + (1-y_{1})^{2} }\\13^{2} = 12^{2} + (1-y_{1})^{2} \\169 = 144 +(1-y_{1})^{2}\\169-144 = (1-y_{1})^{2}\\25 = 1 -2y_{1} +y_{1}^{2} \\y_{1}^{2} -2y_{1}+1-25 =0\\y_{1}^{2} -2y_{1}-24 =0\\y_{1}^{2} -6y_{1} + 4y_{1} -24 =0 \\y_{1}(y_{1}-6) +4(y_{1} -6) = 0\\(y_{1}+4)(y_{1}-6) =0\\(y_{1}+4)=0 or (y_{1}-6) =0[/tex]
[tex]y_{1}+4= 0[/tex] or [tex]y_{1}-6 =0[/tex]
[tex]y_{1} =-4[/tex] or [tex]y_{1} = 6[/tex]
Hence, the possible coordinates of point A are (-8,-4) or (-8,6)