Let line $t$ be the line represented by $3x+4y = 5$ and let line $p$ be the line perpendicular to line $t$ and

Question

Let line $t$ be the line represented by $3x+4y = 5$ and let line $p$ be the line perpendicular to line $t$ and containing the point $(5,5)$. What is the $x$-coordinate of the point common to line $t$ and line $p$? Express your answer as a common fraction.

GPT-5 mini · Answer

The slope of t is -3/4, so the perpendicular slope is 4/3. Line p through (5,5) is y-5 = (4/3)(x-5), i.e. y = 4/3 x - 5/3. Solve with 3x+4y=5:
3x + 4(4/3 x - 5/3) = 5 → 25/3 x - 20/3 = 5 → 25x = 35 → x = 7/5.

Answer: 7/5.

Let line $t$ be the line represented by $3x+4y = 5$ and let line $p$ be the line perpendicular to line $t$ and containing the point $(5,5)$. What is the $x$-coordinate of the point common to line $t$ and line $p$? Express your answer as a common fraction.

All Answers 1

Submit Your Answer