Respuesta :
Answer:
The correct answers for the possible locations for the are;
(-9, 1)
(0, 0)
Step-by-step explanation:
The coordinates of two of the three posts are given in feet as (-5, 4) and (2, 6)
The length of the available fencing = 25 feet
The length, l, of the segment between the coordinates of the two old posts vertices of the fence is given by the following equation;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where;
(x₁, y₁) = (-5, 4)
(x₂, y₂) = (2, 6)
[tex]l = \sqrt{\left (6-4 \right )^{2}+\left (2-(-5) \right )^{2}} = \sqrt{53} \approx 7.25 \ feet[/tex]
Given the coordinates of the third point as (x₃, y₃), we have;
Therefore, we have;
[tex]\sqrt{\left (y_{3}-4 \right )^{2}+\left (x_{3}-(-5) \right )^{2}} + \sqrt{\left (y_{3}-6 \right )^{2}+\left (x_{3}-(2) \right )^{2}} = 25 - \sqrt{53}[/tex]
For the point (2, 6), we have;
[tex]\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 24.2 > 25-\sqrt{53}[/tex]
For the point (-9, 1), we have;
[tex]\sqrt{\left ((-6)-4 \right )^{2}+\left (2-(-5) \right )^{2}} + \sqrt{\left ((-6)-6 \right )^{2}+\left (2-(2) \right )^{2}} = 17.08 < 25-\sqrt{53}[/tex]
For the point (0, 0), we have;
[tex]\sqrt{\left ((0)-4 \right )^{2}+\left (0-(-5) \right )^{2}} + \sqrt{\left ((0)-6 \right )^{2}+\left (0-(2) \right )^{2}} = 12.73 < 25-\sqrt{53}[/tex]
For the point (8, 8), we have;
[tex]\sqrt{\left ((8)-4 \right )^{2}+\left (8-(-5) \right )^{2}} + \sqrt{\left ((8)-6 \right )^{2}+\left (8-(2) \right )^{2}} = 19.92 > 25-\sqrt{53}[/tex]
For the point (-4, -5), we have;
[tex]\sqrt{\left ((-5)-4 \right )^{2}+\left ((-4)-(-5) \right )^{2}} + \sqrt{\left ((-5)-6 \right )^{2}+\left ((-4)-(2) \right )^{2}} = 22.04 > 25-\sqrt{53}[/tex]
Therefore, the correct answers for the possible locations for the are (-9, 1) and (0, 0).
