Moderate -0.3 This is a straightforward coordinate geometry question requiring standard techniques: finding the midpoint of AB, determining the perpendicular gradient (negative reciprocal of -5/4), and writing the equation in point-gradient form. While it involves multiple steps, each is routine and the question provides the line equation explicitly, eliminating any need for problem-solving or insight beyond applying memorized procedures.
The point \(A\) has coordinates \((-1, a)\) and the point \(B\) has coordinates \((3, b)\)
The line \(AB\) has equation \(5x + 4y = 17\)
Find the equation of the perpendicular bisector of the points \(A\) and \(B\).
[4 marks]
Question 4:
4 | Uses negative reciprocal to
obtain equation with correct
gradient | 3.1a | M1 | −4x+5y =k
x=1
⇒5+4y =17
⇒ y =3
k =−4×1+5×3=11
5y−4x=11
4 11
y = x+
5 5
Obtains correct x coordinate of
midpoint
Or obtains correct equations of
lines through A and B
perpendicular to AB
5y−4x=31.5 5y−4x=−9.5
OE | 1.1b | B1
Substitutes their mid-point value
of x to obtain value of y
coordinate of midpoint (not in
terms of a or b)
Or
a+b
Finds a value for their
2
Or
Finds k by adding correct
equations of lines through A and
B perpendicular to AB
Or equating intercepts. | 1.1a | M1
Obtains correct equation ACF
4
Eg y = x+c, c=2.2
5
ISW once correct answer seen. | 1.1b | A1
Total | 4
Q | Marking instructions | AO | Mark | Typical solution
The point $A$ has coordinates $(-1, a)$ and the point $B$ has coordinates $(3, b)$
The line $AB$ has equation $5x + 4y = 17$
Find the equation of the perpendicular bisector of the points $A$ and $B$.
[4 marks]
\hfill \mbox{\textit{AQA Paper 1 2019 Q4 [4]}}