Question

the coordinates of the mid point of the line joining the point 2p+2,3 and 4,2q+1 are 2p,2q find the values of p and q

Answer 1

Mid point of the line joining the points (2p+2,3) and (4,2q+1) = (2p, 2q)

We know that, midpoint of a line joining the points and is

(\frac{X1+X2}{2} ,\frac{Y1+Y2}{2})(

2

X1+X2

,

2

Y1+Y2

)

\small \Rightarrow \left (\frac{2p+2+4}{2}(

2

2p+2+4

,\frac{3+2q+1}{2} \right ) )) =(2p,\ 2q)(2p, 2q)

Comparing the corresponding terms

\small \Rightarrow \frac{2p+6}{2}⇒

2

2p+6

=2p \quad and \quad \frac{4+2q}{2}2pand

2

4+2q

=2q2q

⇒ 2p +6 = 4p and 4+2q = 4q

⇒ 4p - 2p = 6 and 4q - 2q =4

⇒ 2p = 6 and 2q = 4

∴ p = 3 and q = 2

Step-by-step explanation:

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