Question

The points P(0, 6), Q(-5, 3) and R(3, 1) are the vertices of a triangle, which is

(a) equilateral (b) isosceles (c) scalene (d) right angeled

Answer 1

Let the vertices be P(0,6); Q(-5,3) and R(3,1).
Remember that in a right triangle Pythagoras theorem will be followed.
Also for an isosceles triangle two sides must be of the same length.
By distance formula:

$PQ=\sqrt{(}(0--5{)}^2+(6-3{)}^2)=6unit$

$QR=\surd \left(\right(3-(-5){)}^2+(1-3{)}^2)=\sqrt{6}8=2\sqrt{1}7unit$

$RP=\surd \left(\right(3-0{)}^2+(1-6{)}^2)=6unit$
The triangle is clearly isosceles as $PQ=RP$
Also,
$P{Q}^2+P{R}^2$
$=36+36$
$=72\ne Q{R}^2$

(b) isosceles