Question

Here's a question ~

Answer 1

Answer:

• (0, 5√3/2 + 2)

Step-by-step explanation:

Given is the absolute value function.

Observations:

• 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.

The angle YAP₂ is:

• arctan (1/√3) = 30°

The distance AY is:

• AY = AP₂ cos 30° = 5*√3/2

The distance from the x-axis to the point Y is:

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

The coordinates of the point Y:

• (0, 5√3/2 + 2)