Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find the value of $k$ if&n

Question

Three points have coordinates $A(1, 8)$, $B(0, 3)$ and $C(k, 5)$. Find the value of $k$ if $AC$ is perpendicular to $BC$, the midpoint of $AB$, the equation of the perpendicular bisector of $AB$, the lengths of $AB$ and $BC$, the area of triangle $ABC$, using the results in (d).

Accepted Answer

(a) $k = 3$ or $k = -2$; (b) $\left(\dfrac{1}{2}, \dfrac{11}{2}\right)$; (c) $y = -\dfrac{1}{5} x + \dfrac{28}{5}$; (d) AB $= 5.10$ units, BC $= 3.61$ units when $k = 3$, BC $= 2.83$ units when $k = -2$; (e) area $= 6.5$ square units when $k = 3$, area $= 6$ square units when $k = -2$

Coordinate Geometry - Length of a Line Segment

Coordinate Geometry - Length of a Line Segment

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