The Mid-Point of (3p,4) and (-2,2q) is (2,6) . Find the value of p+q - Bzziii

The mid-point of (3p,4) and (-2,2q) is (2,6) . Find the value of p+q (a) 5 (b) 6 (c) 7 (d) 8
The mid-point of (3p,4) and (-2,2q) is (2,6) . Find the value of p+q 

(a) 5 
(b) 6 
(c) 7 
(d) 8




(b) 6

Explanation:

Coordinates of Mid-Point M = `(\frac{x_{1}+x_{2}}{2}`,`\frac{y_{1}+y_{2}}{2})`

(2, 6) = `(\frac{3p + (- 2)}{2}`,`\frac{4 + 2q}{2})`

(2, 6) = `(\frac{3p - 2}{2}`,`\frac{2q + 4}{2})`

x- Coordinate

⇒ 2 = `"3p - 2"/"2"`

⇒ 2`\times` 2 = 3p - 2

⇒ 4 = 3p - 2

⇒ 4 + 2 = 3p

⇒ 6 = 3p

⇒ 3p = 6

⇒ p = `6/3`

∴ p = 2

Now,
y - Coordinate

⇒ 6 = `"2q + 4"/"2"`

⇒ 6`\times` 2 = 2q + 4

⇒ 12 = 2q + 4

⇒ 12 - 4 = 2q

⇒ 8 = 2q

⇒ 2q = 8

⇒ q = `8/2`

∴ q = 4

Thus,

⇒ p + q = 2 + 4

= 6





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