Respuesta :
Answer:
k = -3 or 5
Step-by-step explanation:
The given parameters are;
The line extends from points (-1, 1) to point (2, k)
The length of the line = 5 units
The formula for the length, l, of a line given its coordinates can be found by the following formula;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, we have;
[tex]5 = \sqrt{\left (k-1 \right )^{2}+\left (2-(-1) \right )^{2}}[/tex]
Which, by squaring both sides, gives;
25 = (k - 1)² + (2 - (-1))² = (k - 1)² + (2 + 1)² = (k - 1)² + 3²
25 = (k - 1)² + 3² = k² - 2·k + 1 + 9
25 - 25 = 0 = k² - 2·k + 1 + 9 - 25 = k² - 2·k - 15
0 = k² - 2·k - 15
0 = (k +3) × (k - 5)
Therefore, k = -3 or 5
When k - -3, we have;
[tex]\sqrt{\left ((-3)-1 \right )^{2}+\left (2-(-1) \right )^{2}}= \sqrt{(-4)^2+3^2} = \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
When k = 5, we have;
[tex]\sqrt{\left (5-1 \right )^{2}+\left (2-(-1) \right )^{2}}= \sqrt{4^2+3^2} = 5[/tex]
