Question

Which of the following coordinates belong in the box?

Answer 1

Since the distance from the two known coordinates are known, you can find the slope of the line (for lack of a better word) to work backwards. there is a +5 unit gap between -21 and -16, so the next number would be -26. So, without havint to do any more work, the answer is B.

Answer 2

Answer: The correct option is (B) (-26, -5).

Step-by-step explanation: We are given to select the correct co-ordinates that belong in the box.

As shown in the given figure, we can see that

the points with co-ordinates (-21, -9) is the mid-point of the point with co-ordinates that belong in the box and the point with co-ordinates (-16, -13.)

Let, (a, b) be the co-ordinates that belong in the box.

Then, from the mid-point formula, we have

`(-21,-9)=\left((a+(-16))/(2),(b+(-13))/(2)\right)\\\\\\\Rightarrow (-21,-9)=\left((a-16)/(2),(b-13)/(2)\right)\\\\\\\Rightarrow -21=(a-16)/(2),~~~~~~~~~-9=(b-13)/(2)\\\\\\\Rightarrow a-16=-42~~~~~~~~~~~~~\Rightarrow b-13=-18\\\\\\\Rightarrow a=-42+16,~~~~~~~~~~~~\Rightarrow b=-18+13\\\\\Rightarrow a=-26~~~~~~~~~~~~~~~~~~~~\Rightarrow b=-5.`

Thus, the co-ordinates that belong in the box are (-26, -5).

Option (B) is CORRECT.