8. WMA11/01 Edexcel IAL P1 January 2022, Q8 (Straight Line Graphs & Equations and Inequalities: Simultaneous Equations)
The line l1 has equation
2x – 5y + 7 = 0
(a) Find the gradient of l1
(1)
Given that
the point A has coordinates (6, –2)
the line l2 passes through A and is perpendicular to l1
(b) find the equation of l2 giving your answer in the form y = mx + c, where m and c are constants to be found.
(3)
The lines l1 and l2 intersect at the point M.
(c) Using algebra and showing all your working, find the coordinates of M.
(Solutions relying on calculator technology are not acceptable.)
(3)
Given that the diagonals of a square ABCD meet at M,
(d) find the coordinates of the point C.
(2)
SOLUTION
a-
On comparing the above equation with the general equation of a straight line y=mx+c, the gradient of line is
b- Since l2 is perpendicular to l1, the gradient of l2 is given as
Using point-slope formula to find the equation of line l2, where point the passes through is A (6, -2) & gradient is -5/2.
c- To find the point of intersection, solve both equation of lines siumultaneously.
Where, the equation of l1 is
And, the equation of l2 is
On solving through substitution method, it gives
Now, putting it back to either equation of lines. Here we are substituting in the equation of l1
Hence, the point of intersection M is
d-
Always remember that square is one of the shapes whose diagonals cuts at the midpoint. Now, using this property, applying the formula of mid-point.
Thus, the coordinates of point C is given as
