Find the line through the midpoint of A(3,−8), B(−7,4), perpendicular to 3x−4y+14=0.

01 / Standard#Your turn

Official paper · jm01-2023 · I.11 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Average the coordinates.

Hint 2

Use the negative reciprocal slope.

Worked solution

Checks and common pitfalls: The perpendicular slope changes sign as well as taking a reciprocal.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The midpoint is (−2,−2); the required slope is −4/3.
$m_0=3/4,\quad m=-4/3$
Use point-slope form.
$y+2=-\frac43(x+2)\iff4x+3y+14=0$

Think first. Reveal a hint when the class is ready.

2023 JM01