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Can the verb "lie" be a transitive when it's used in the sense of "to occupy a certain relative place"?

My son's math book had the following task:

If the maximum point of y = ax² + bx + 1 is (3 , 4) , which quadrant lies (a , b)?

I was a bit puzzled by this usage of "lie" here. Shouldn't it be rather used with preposition "at"? Like here:

If the maximum point of y = ax² + bx + 1 is (3 , 4) , which quadrant lies at (a , b)?

Or is it like "to lie at a point" and "to lie a point" are two different phrases with two different meanings?

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  • 5
    It's a mistake. They've missed out "in": in which quadrant lies (a,b).
    – Colin Fine
    Commented Dec 22, 2021 at 15:38
  • 2
    and "in which quadrant does (a, b) lie?" would be significantly clearer, IMO
    – David Siegel
    Commented Dec 22, 2021 at 16:55
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    What @DavidSiegel said. The point (a,b) lies in some quadrant. It makes no sense to say the quadrant lies in the point.
    – FumbleFingers
    Commented Dec 22, 2021 at 18:15

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I add the in, as @Colin Fine has commented.

If the maximum point of y = ax² + bx + 1 is (3 , 4), [in] which quadrant lies (a , b)?

lie in this case is intransitive, as explained below.

B1 [ I + adv/prep, L ] present participle lying | past tense lay | past participle lain If something lies in a particular place, position, or direction, it is in that place, position, or direction.

reference

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