Question

For Points P=(x_1,y_1) and Q(x_2,y_2) of the coordinate plane a new distance d(P,Q) is defined by d(P,Q) = |x_1 - x_2|+|y_1-y_2| Let O = (0,0) and A = (3,2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray . Sketch this set in a labelled diagram. (10 marks)

Answer 1

The hardest part of this question is the language :/

Answer 2

I swear :P

Answer 3

using the new distance definition, then for some point (x,y)
setting the distance equal to both O and A
\[\rightarrow |x| +|y| = |x-3| +|y-2|\]
now to show that is a union of line segment and ray ...

Answer 4

hmm not a fan of absolute value functions

Answer 5

|x| + |y| = |x-3| + |y-2|
Since it's the first quadrant, x and y shall be positive.
x + y = |x-3| + |y-2|
Now up till (2,2)
The line should be x+y = -x + 3 - y + 2
2x + 2y = 5

Answer 6

Is this right?

Answer 7

yes. It is right. But I am facing the problem in understanding this question.

Answer 8

@Ishaan94 and @dumbcow , how would you proceed further??

Answer 9

Hmm they (the question) have defined a new distance formula.

Answer 10

And we are supposed to get the points which are equidistant from the points O and A, using the new distance formula. Is that right? @dumbcow

Answer 11

correct

Answer 12

It should be the ditsnace individually. Suppose. See the dig below
Like distance between O and P (by new distance formula) should be equal to distance between A and Q (by new distance formula)