Question

please solve this question​

Answer 1

$\huge{\underline{\underline{\bf Formula:-}}}$

$\underline\green{\boxed{\bf Distance\: Formula = \sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}}}$

$\huge{\underline{\underline{\bf Required\: Solution}}}$

(ii) Distance between car and petrol pump

$\implies$ Coordinates of car = (7,3)

$\implies$ Coordinates of petrol pump = (-4,-3)

$\implies \sf distance = \sqrt{ {( - 4 - 7)}^{2} + {( - 3 - 3)}^{2} } \\ \\ \implies \sf \: distance = \sqrt{ {( - 11)}^{2} + {( - 6)}^{2} } \\ \\ \implies \sf \: distance = \sqrt{121 + 36} = \sqrt{157} = 12.5$

So, the distance is 12.5 units which is approx 13 units.

(iv) Difference of given distances.

$\implies$ Coordinates of Car = (7,3)

$\implies$ Coordinates of petrol pump = (-4,-3)

$\implies$ Coordinates of Landmark = (-4,4)

Distance between car and petrol pump via landmark = Distance between car and landmark + Distance between petrol pump and landmark

Direct distance between car and landmark:-

$\implies\sf distance = \sqrt{( - 4 - 7)^{2} + \sqrt{(4 - 3)}^{2} } \\ \\ \implies\sf \: distance = \sqrt{ { (- 11)}^{2} + {1}^{2} } \\ \\ \implies\sf \: distance = \sqrt{121 + 1} = \sqrt{122} = 11$

Distance between landmark and petrol pump :-

$\implies\sf \: distance = \sqrt{ {(( - 4 - ( - 4))}^{2} + {(4 - ( - 3))}^{2} } \\ \\ \implies\sf \: distance = \sqrt{ { (- 4 + 4)}^{2} + (4 + 3)^{2} } \\ \\ \implies\sf \: distance = \sqrt{0 + 7^{2} } = \sqrt{49} = 7 \\ \\ \implies\sf \therefore \: total \: distances = 11 + 7 = 18$

Difference between short cut and long cut :-

Long cut - Short cute = 18-13 = 5

hence, 5 units is the required answer.

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I guess last part is quite wrong. Kindly recheck the Ques. and ask.