IB Mathematics Applications & Interpretation Topic SL…

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

Find the equation of line $AB$ and the length of the segment $PQ$ .

On a coordinate map, two emergency beacons are at $P(-5, 4)$ and $Q(1, -2)$ . The boundary separating their signal zones is the set of all points equidistant from $P$ and $Q$ .

Sites are $A(-3,1)$ and $B(5,5)$ . Facility $P$ lies on their perpendicular bisector and on $x+y=2$ .

The map uses perpendicular coordinates in kilometres.

A surveyor records two chords of a circular display boundary. Their endpoints are $A=(-4,0)$ , $B=(4,0)$ and $C=(-2,6)$ , $D=(4,4)$ , with coordinates in metres.

(a) the perpendicular bisector of each chord.

(b) Hence the centre and radius of the circle.

On a map with perpendicular coordinates in kilometres, two sites are $A=(a,0)$ and $B=(0,a)$ , where $a\gt0$ . A facility $P$ lies on their perpendicular bisector and on $2x+y=12$ . Its distance from $A$ is 5 kilometres.

the equation of this boundary, expressing your answer in the form $y = mx + c$ .

(a) the perpendicular bisector and hence the coordinates of $P$ .

(b) the common distance from $P$ to the two sites.

(c) Site $B$ moves horizontally to $B_t(t,5)$ . all values of $t$ for which $P$ remains equidistant from $A$ and $B_t$ , and the two solutions.

(a) Show that the perpendicular bisector is independent of $a$ , and hence $P$ .

(b) both possible values of $a$ .

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 3.5—intersection of Lines, Equations of Perpendicular Bisectors Questionbank