Moderate -0.8 This is a straightforward AS-level coordinate geometry question requiring students to find the gradient of l₂ from two points, rearrange l₁ into y = mx + c form to find its gradient, then compare gradients using standard rules (equal for parallel, product = -1 for perpendicular). It involves only routine techniques with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple steps and careful arithmetic.
The line \(l_1\) has equation \(2x - 3y = 9\)
The line \(l_2\) passes through the points \((3, -1)\) and \((-1, 5)\)
Determine, giving full reasons for your answer, whether lines \(l_1\) and \(l_2\) are parallel, perpendicular or neither.
States the gradient of line \(l_1\) correctly; Attempts to find gradient of line joining \((3, -1)\) and \((-1, 5)\); Attempts the product of \(m_1\) and \(m_2\); States that lines \(l_1\) and \(l_2\) are perpendicular
Lines $l_1$ and $l_2$ are perpendicular | B1, M1, M1, A1 | States the gradient of line $l_1$ correctly; Attempts to find gradient of line joining $(3, -1)$ and $(-1, 5)$; Attempts the product of $m_1$ and $m_2$; States that lines $l_1$ and $l_2$ are perpendicular
The line $l_1$ has equation $2x - 3y = 9$
The line $l_2$ passes through the points $(3, -1)$ and $(-1, 5)$
Determine, giving full reasons for your answer, whether lines $l_1$ and $l_2$ are parallel, perpendicular or neither.
\hfill \mbox{\textit{Edexcel AS Paper 1 Q4}}