Problem Solving

In the standard coordinate system, which of the following points is the greatest distance from the origin:

(A) (-4, -1)
(B) (-3, 3)
(C) (4, 0)
(D) (2, 3)
(E) (0, 4)

The OA is B.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

In the standard coordinate system, which of the following points is the greatest distance from the origin:

(A) (-4, -1)
(B) (-3, 3)
(C) (4, 0)
(D) (2, 3)
(E) (0, 4)

The OA is B.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hi Swerve,
Let's take a look at your question.

We are given some points and we need to find out which of the points is the greatest distance from the origin.
The distance can be calculated using the distance formula as stated below:
$$\left(Distance\right)^2=\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2$$

Let's find the distance of each point from the origin.

OPTION A:
(-4, -1)
$$\left(Distance\right)^2=\left(-4-0\right)^2+\left(-1-0\right)^2$$
$$\left(Distance\right)^2=16+1=17$$

OPTION B:
(-3, 3)
$$\left(Distance\right)^2=\left(-3-0\right)^2+\left(3-0\right)^2$$
$$\left(Distance\right)^2=9+9=18$$

OPTION C:
(4, 0)
$$\left(Distance\right)^2=\left(4-0\right)^2+\left(0-0\right)^2$$
$$\left(Distance\right)^2=16+0=16$$

OPTION D:
(2, 3)
$$\left(Distance\right)^2=\left(2-0\right)^2+\left(3-0\right)^2$$
$$\left(Distance\right)^2=4+9=13$$

OPTION E:
(0, 4)
$$\left(Distance\right)^2=\left(0-0\right)^2+\left(4-0\right)^2$$
$$\left(Distance\right)^2=0+16=16$$

Now, we can see that the square of the distance from the origin is greatest Option B.
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.