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Three-Dimensional Geometry · Question 58 of 120

What is the image of P in L?

Question 58

HardOriginal question

A point $P(5, 1, 4)$ and the line $L: \frac{x - 1}{2} = \frac{y}{2} = \frac{z - 3}{-1}$ are given. $M$ is the point of $L$ with parameter $\lambda$ , and $F$ is the foot of the perpendicular from $P$ to $L$ .

What is the image of $P$ in $L$ ?

(3, 2, 2)

Correct answerYour answer

(7, 0, 6)

Correct answerYour answer

(11, 5, 8)

Correct answerYour answer

(1, 3, 0)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$F$ is the midpoint of $P$ and its image $P'$ , so $P' = 2F - P$ .
$P' = (6 - 5, 4 - 1, 4 - 4) = (1, 3, 0)$ .

Worth noting

$(3, 2, 2)$ is the foot $F$ , only halfway to the image.

Concept: The image of a point in a line
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsThe equation of a line

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