Question

. On a coordinate grid, the location of a bank is (–4, 8) and the location of a post office is (2, 0).

The scale used is 1 unit = 50 m. What is the shortest possible distance between the bank and the

post office?
​

Answer 1

Distance formula:

If $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points, then the distance between them is given by

$d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$ units

Solution:

• The given points are $(-4,8)$ and $(2,0)$.

• The distance between them is

• $=\sqrt{(-4-2)^{2}+(8-0)^{2}}$ units

• $=\sqrt{(-6)^{2}+8^{2}}$ units

• $=\sqrt{36+64}$ units

• $=\sqrt{100}$ units

• $=10$ units

• Since it is given that $1$ unit = $50$ m, the actual shortest possible distance between the bank and the post office is $(10\times 50)$ m = $500$ m.

Answer:

• Shortest possible distance is 500 m.

Answer 2

SOLUTION

GIVEN

• On a coordinate grid, the location of a bank is (–4, 8) and the location of a post office is (2, 0)

• The scale used is 1 unit = 50 m

TO DETERMINE

The shortest possible distance between the bank and the post office

FORMULA TO BE IMPLEMENTED

$\sf{The \: Distance \: between \: two \: points \: (x_1,y_1) and (x_2,y_2) \: is\: }$

$= \sf{ \sqrt{{(x_2-x_1)}^{2} +{(y_2-y_1)}^{2}} } \: \: \: unit$

EVALUATION

Let us first plot the points in paper in coordinate system ( Refer to the attachment )

Let the position of bank is A ( - 4, 8 ) & the position of post office is B ( 2, 0 )

From the figure it is clear that the shortest distance between bank & post office is

$\sf{AB \: = \sqrt{ {( - 4 - 2)}^{2} + {(8 - 0)}^{2} } } \: \: \: \: unit$

$\implies\sf{AB \: = \sqrt{36 + 64} } \: \: \: unit$

$\implies\sf{AB \: = 10}\: \: \: unit$

Now The scale used is 1 unit = 50 m

Hence the shortest distance between bank & post office

$= \sf{(10 \times 50) \: \: metre}$

$\sf{ = 500 \: metre}$

FINAL ANSWER

The shortest possible distance between the bank and the post office = 500 metre

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