Question

Which of the following coordinates belong in the box?

Answer 1

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

$(-21,-9)=\left(\dfrac{a+(-16)}{2},\dfrac{b+(-13)}{2}\right)\\\\\\\Rightarrow (-21,-9)=\left(\dfrac{a-16}{2},\dfrac{b-13}{2}\right)\\\\\\\Rightarrow -21=\dfrac{a-16}{2},~~~~~~~~~-9=\dfrac{b-13}{2}\\\\\\\Rightarrow a-16=-42~~~~~~~~~~~~~\Rightarrow b-13=-18\\\\\\\Rightarrow a=-42+16,~~~~~~~~~~~~\Rightarrow b=-18+13\\\\\Rightarrow a=-26~~~~~~~~~~~~~~~~~~~~\Rightarrow b=-5.$

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

Option (B) is CORRECT.

Answer 2

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.