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i need help (A level maths)(coordinate geometry)

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the question says that

p>q>0

find the length of the line segment joining these paris of points.

(p , q) and (q , p)

these are the coordinates.

there must some formula or something that i dont know.

$$\sqrt{(p-p)^2 + (q-q)^2}$$

and if the answer from the back of the book is required i will post it

ALL HELP IS DEEPLY APRECIATED

Jul 17, 2018
edited by Scarface3010  Jul 17, 2018
edited by Scarface3010  Jul 17, 2018

#1
+2

the question says that

p>q>0

find the length of the line segment joining these pairs of points.

(p , q) and (q , p)

these are the coordinates.

$$\begin{array}{|rcll|} \hline \text{length} &=& \sqrt{(p-q)^2+(q-p)^2} \\ &=& \sqrt{(p-q)^2+\Big(-(p-q)\Big)^2 } \\ &=& \sqrt{(p-q)^2+\Big( (-1)(p-q) \Big)^2 } \\ &=& \sqrt{(p-q)^2+(-1)^2(p-q)^2 } \quad & | \quad (-1)^2 = 1^2 = 1 \\ &=& \sqrt{(p-q)^2+1\cdot(p-q)^2 } \\ &=& \sqrt{(p-q)^2+(p-q)^2 } \\ &=& \sqrt{2\cdot (p-q)^2 } \\ &\mathbf{=}& \mathbf{(p-q)\sqrt{2}} \\ \hline \end{array}$$ Jul 17, 2018
#2
+2

Thanks Heureka,

Scarface, the formula that you used was incorrect.  Heureka's one is right.

This is the formula that it comes from

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

this is the distance forumla which kids are told to learn.

It looks horrible but it is just Pythagoras's theorum.   :)

Jul 17, 2018