I have figured out some of the questions. I'm stuck on the last one.

Q: The line AB has equation 3x+5y=8 and the point A has coordinates (6,-2).

a) i) find the gradient of AB

ANS: -3/5

ii) Hence find the equation of the straight line which is perpendicular to AB and which passes through A.

ANS: 5x-3y=36

b) The line AB intersects the line with equation 2x+3y=3 at point B. Find the coordinates of B.

ANS: (-9,7)

c) The point C has coordinates (2,k) and the distance from A to C is 5. Find the two possible values of the constant k.

---I don't know how to work out c). Any directions/advice would be extremely helpful. Thanks in advance!----

## Answers (1)

Distance between points (a, b) and (c, d) is given by the equation

(a - c)² + (b - d)² = distance²

Therefore,

(6 - 2)² + (-2 - k)² = 5²

4² + (4 + 4k + k²) = 25

Rearranging :

k² + 4k - 5 = 0

(k - 1) (k + 5) = 0

hence k = 1 or k = -5

Now substitute these values into the formula (6 - 2)² + (-2 - k)² to check them.