Question

The coordinates of the points M, N, P, and Q are -11, 32, -15, and 17, respectively. Which point is closest to the origin?

A. P

B. M

C. N

D. Q

Answer 1

@DuarteME

Answer 2

The distance between two points \(A\) with coordinate \(x_\textrm{A}\) and \(B\) with coordinate \(x_\textrm{B}\) is:
\(d_{BA} = |x_\textrm{A}-x_\textrm{B}|\)

Now take \(B=O \implies x_\textrm{B} = x_\textrm{O} = 0\), where \(O\) is the origin. The distance from \(A\) to the origin \(O\) is therefore:
\(d_{OA} = |x_\textrm{A}|.\)

This means you simply need to look at the coordinates and remove their signs. Finally, since you want the one closer to the origin (i.e., with smaller \(d_{OA}\)), you choose the smaller value.

Then again, you can also draw a number line and mark the points and the origin and conclude the same thing. \(\ddot{\smile}\)

Answer 3

B

Answer 4

IS IT B

Answer 5

Yes, it is. \(\ddot{\smile}\)

Answer 6

Point M is at what location on the number line?

https://i.imgur.com/6QI8XEf.jpg





A. -1/ 2

B. -2

C. -1

D. −1 1/2

Answer 7

Just notice that the coordinate of \(M\) is between \(-2\) e \(-1\), i.e., \(-2 < x_\textrm{M} < -1\).
Which of the options represents such a number?

Answer 8

it would be A

Answer 9

Are you sure? Notice that \(-\dfrac{1}{2}\) is not between \(-2\) and \(-1\). It is actually between \(-1\) and \(0\).

Answer 10

oh ok, it's D

Answer 11

That is correct. \(\ddot{\smile}\)

Answer 12

thank you