SL 3.5—Intersection of lines, equations of perpendicular bisectors Questionbank

The line joining the points $A(2,-4)$ and $B(6,8)$ meets the $x$ - and $y$-axes at the points $P$ and $Q$, respectively.

The line through the point $A(2,-3)$ is perpendicular to the line $2 x+y=5$. This new line intersects the $x$-axis at point $P$ and the $y$-axis at point $Q$.

Given that the points $A(2,1), B(t, 2 t)$, and $C\left(t^{2}, 5 t-3\right)$ are collinear, find all possible values of $t$.

The equations of the sides $A B, B C$, and $C A$ of triangle $A B C$ are given as:

The straight line passing through the points $(1,4)$ and $(7,-2)$ intersects the line $x+2 y=10$ at the point $P$.

Find the gradient of the line that passes through the points $\mathrm{A}(2,3)$ and $\mathrm{B}(6$, 7).

A line passes through the point $\mathrm{P}(2,-1)$ and has a gradient of 3 .

Calculate the perpendicular distance from the point $P(2,5)$ to the line joining the points $A(1,-2)$ and $B(5,4)$.

Determine the coordinates of the midpoint of the segment joining $\mathrm{A}(4,2)$ and $\mathrm{B}(10,8)$.

In a city park, three security cameras are positioned at points A(1,4), B(4,1), and C(7,6) to monitor different areas. To optimize coverage, the park administration wants to find the point equidistant from cameras A and B and analyze its significance for park security.