Using the distance between two points, it is found that the values of k are given by:
c. -3, -7
Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this problem, the points are: (-5, 5) and (k,0).
They are a distance of [tex]D = \sqrt{29}[/tex] apart, hence:
[tex]\sqrt{29} = \sqrt{(k + 5)^2+ (0 - 5)^2}[/tex]
[tex](\sqrt{29})^2 = (\sqrt{(k + 5)^2+ (0 - 5)^2})^2[/tex]
[tex](k + 5)^2 + (-5)^2 = 29[/tex]
[tex]k^2 + 10k + 21 = 0[/tex]
Which is quadratic equation with coefficients [tex]a = 1, b = 10, c = 21[/tex].
Hence:
[tex]\Delta = b^2 - 4ac = 10^2 - 4(1)(21) = 16[/tex]
[tex]x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-10 - 4}{2} = -7[/tex]
[tex]x_2 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-10 + 4}{2} = -3[/tex]
Hence option c is correct.
You can learn more about distance between two points at https://brainly.com/question/18345417
