Question

21. The distance between the points A(1, 2k) and B(1-k. 1) is √11-9k. Find the possible values

of k.

Answer 1

The possible values of k are 2.5 and 1.

Step-by-step explanation:

To find the distance between the points A(1, 2k) and B(1-k, 1), we can use the distance formula.

The distance formula is given by: d = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates of points A and B, we can substitute them into the formula and simplify:

1. d = √((1 - (1 - k))^2 + (1 - 2k)^2)
2. d = √(k^2 + (1 - 2k)^2)

Since the given distance between A and B is √(11 - 9k), we can equate it to the distance formula and solve for k:

√(11 - 9k) = √(k^2 + (1 - 2k)^2)

Squaring both sides, we get:

11 - 9k = k^2 + (1 - 2k)^2

Simplifying further, we have:

11 - 9k = k^2 + (1 - 4k + 4k^2)

Combining like terms and rearranging the equation:

4k^2 - 13k + 10 = 0

Factoring the quadratic equation, we can determine the possible values of k:

1. (2k - 5)(2k - 2) = 0
2. 2k - 5 = 0 or 2k - 2 = 0
3. k = 2.5 or k = 1

Therefore, the possible values of k are 2.5 and 1.

Learn more about Finding the distance between two points on a coordinate plane