If M(4, 5) is the mid-point of the line segment joining the points A(\(k\), 4) and B(7, \(-3p\)), then find the value of \(2k+3p\).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -4
The mid-point of the segment joining \((x_1,y_1)\) and \((x_2,y_2)\) is \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\), so each coordinate of M gives one equation.
From the x-coordinates: \(\displaystyle\frac{k+7}{2}=4\), so \(k+7=8\) and \(k=1\)
From the y-coordinates: \(\displaystyle\frac{4-3p}{2}=5\), so \(4-3p=10\) and \(p=-2\)
Putting both values in: \(2k+3p=2(1)+3(-2)=2-6=-4\)