Question

Which of the following points is farthest from the origin?


(–6, 8)


(3, –4)


(4, –3)


(4, –2)

Answer 1

Answer:

the farthest point is

-6,8

Answer 2

The correct answer is (-6, 8).

Given: Points = (-6, 8), (3, –4), (4, –3) and (4, –2).

To Find: Farthest point from the origin.

Solution:

Origin = (0, 0).

Distance formula = $\sqrt{(x_{2} -x_{1} )^{2}+ (y_{2} -y_{1} )^{2}}$.

Calculating for point  (-6, 8) and (0, 0).

= $\sqrt{(-6-0 )^{2}+ (8-0 )^{2}}$

= $\sqrt{(-6 )^{2}+ (8 )^{2}}$

= $\sqrt{36+64}$

= $\sqrt{100}$

= 10

Calculating for point  (3, -4) and (0, 0).

= $\sqrt{(3-0 )^{2}+ (-4-0 )^{2}}$

= $\sqrt{(3 )^{2}+ (-4 )^{2}}$

= $\sqrt{9+16}$

= $\sqrt{25}$

= 5

Calculating for point  (4, -3) and (0, 0).

= $\sqrt{(4-0 )^{2}+ (-3-0 )^{2}}$

= $\sqrt{(4 )^{2}+ (-3 )^{2}}$

= $\sqrt{16+9}$

= $\sqrt{25}$

= 5

Calculating for point  (4, -2) and (0, 0).

= $\sqrt{(4-0 )^{2}+ (-2-0 )^{2}}$

= $\sqrt{(4)^{2}+ (-2 )^{2}}$

= $\sqrt{16+4}$

= $\sqrt{20}$

= 4.472

So, from 10, 5, 5 and 4.472, 10 is the largest number.

Hence, the farthest point from the origin is (–6, 8).

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