Moderate -0.8 This is a straightforward two-step question requiring the midpoint formula and substitution into a linear equation. Both are routine C1 techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires correct execution of both steps.
A is the point \((1, 5)\) and B is the point \((6, -1)\). M is the midpoint of AB. Determine whether the line with equation \(y = 2x - 5\) passes through M. [3]
Question 3:
3 | 1 6 5 1
midpt M of AB = , oe isw soi
2 2
subst of their midpt into y = 2x 5 and
attempting to evaluate
all work correct and ‘Yes’ oe | M1
M1
A1
[3] | condone lack of brackets; accept in the form
x = 7/2 oe, y = 2 oe
eg 2 × their 3.5 5 = their result
accept 2 = 2 × 3.5 5 | alt methods: allow 2nd M1 for finding
6x 31
correct eqn of AB as y oe
5 5
and attempting to solve as simult eqn
with y = 2x 5 for x or y
or
allow M1 for finding in unsimplified
form the eqn of the line through their
midpt with gradient 2 and A1 for
showing it is y = 2x 5, so Yes
A is the point $(1, 5)$ and B is the point $(6, -1)$. M is the midpoint of AB. Determine whether the line with equation $y = 2x - 5$ passes through M. [3]
\hfill \mbox{\textit{OCR MEI C1 Q3 [3]}}