DᴀʀᴋPᴀʀᴀᴅᴏx
contestada

Here's a question ~

p1 and p2 are points on either of the two lines

[tex]y - \sqrt{3} |x| = 2[/tex]

at a distance of 5 units from their point of point of intersection. Find the coordinates of the foot of perpendiculars drawn from p1 , p2 on the bisector of the Angle between the given lines.​

Respuesta :

mhanifa

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)
Ver imagen mhanifa

Otras preguntas