Question

F (a,d) ,a (c,d), s(c,b) and t(a,b) are distinct points on the coordinate plane. is fs=at? justify your answer.

Answer 1

F (a,d) ,A (c,d), S(c,b) and T(a,b) are distinct points on the coordinate plane. Then FA=ST

Step-by-step explanation:

For any two points in a two dimensional plane (a,b) and (c,d), the distance between the is $\sqrt{{(a-c)^{2}+(b-d)^{2}}$.

Now consider the points F(a,d) and A(c,d).

The distance between them is, $FA=\sqrt{(a-c)^{2}+(d-d)^{2}} \\\\~~~~~=\sqrt{(a-c)^{2}} \\~~~~~=\sqrt{(c-a)^{2}}$ (since the square of (a-c) and (c-a)  are same).

Similarly consider the points S(c,b) and T(a,b).

The distance between them is, $ST=\sqrt{(c-a)^{2}+(b-b)^{2}} \\\\~~~~~=\sqrt{(c-a)^{2}}$

Therefore the distances FA and ST are same.