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Makovka662 [10]
3 years ago
13

Here's a question ~

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0

Answer:

  • (0, 5√3/2 + 2)

Step-by-step explanation:

Given is the absolute value function.

<u>Observations:</u>

  • It has a slope of ±√3 and the y- intercept of 2.
  • There is no horizontal shift, so the the y-axis is the line of symmetry.
  • The y-axis is also an angle bisector of the two lines.
  • The foot P₁P₂ is parallel to the x-axis since it's perpendicular to the y- axis.

We need to find the coordinates of intersection of the line P₁P₂ with the y- axis (the point Y in the picture).

Consider the triangle AYP₂.

We know AP₂ = 5.

<u>The angle YAP₂ is:</u>

  • arctan (1/√3) = 30°

<u>The distance AY is:</u>

  • AY = AP₂ cos 30° = 5*√3/2

<u>The distance from the x-axis to the point Y is:</u>

  • 5√3/2 + 2, added the y- intercept of the graphed lines

<u>The coordinates of the point Y:</u>

  • (0, 5√3/2 + 2)

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