7. Five mark exercise problems - I

1. What is the slope of a line perpendicular to the line joining \(A(5,1)\) and \(P\) where \(P\) is the midpoint of the segment joining \((4,2)\) and \((-6,4)\).

 

Answer:

 

The coordinates of the midpoint \(P\) is $\left(i,i\right)$.

 

Slope of \(AP =\) $\frac{i}{i}$.

 

Slope of the line perpendicular to \(AP\) is .

 

2. The line through the points \((-2,6)\) and \((4,8)\) is perpendicular to the line through the points \((8,12)\) and \((x,24)\). Find the value of \(x\).

 

Answer:

 

The value of \(x\) is .

 

3. If the points \(A(2,2)\), \(B(-2,-3)\), \(C(1,-3)\) and \(D(x,y)\) form a parallelogram then find the value of \(x\) and \(y\).

 

Answer:

 

The value of \(x =\)

 

The value of \(y =\)