The points $A(2,-4)$, $B(2,6)$ and $C(t,6)$, where $t2$, form a triangle of area \(

Question

The points $A(2,-4)$, $B(2,6)$ and $C(t,6)$, where $t>2$, form a triangle of area $30$ square units. Find $t$.[3] Find the equation of the perpendicular bisector of $AB$.[2] Find the equation of the line through $C$ perpendicular to $AB$, and explain why it is not the perpendicular bisector of $AB$.[2]

Accepted Answer

(a) $8$; (b) $y=1$; (c) $y=6$, which does not pass through the midpoint.

A triangle with a vertical side and a given area

A triangle with a vertical side and a given area

Solution:

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