# 3 - General Coordinate Geometry Questions Answers

A(3,4) and B is a variable point on the line |X| = 6. Also, AB ≤ 4. Then the number of positions of B with integral co-ordinates is:

(a)5  (b) 6 (c) 10 (d) 12

Joshi sir comment by diagram (6,4),(6,3),(6,2) are points having AB<4 besides it two upside points are also there by symmetry not shown in diagram. These points are (6,5) and (6,6)

Total no. of points = 5

For which integers n ≥ 3 does there exist a regular n-gon in the plane such that
all of its vertices have integer coordinates?

Joshi sir comment

for n = 4, we can form a square with integral coordinates of all the vertices.

Prove that the four projections of vertex A of the triangle ABC onto the exterior
and interior angle bisectors of  B and  C are collinear.
Joshi sir comment in the given diagram red lines are angle bisectors (interior and exterior)and X, Y, Z, W are the projections of A on these red lines

by angle bisector property all these 4 points will lie on the line BC (either externally or internally) so these points will be in a line