Question

Apoint p lay on a line that is parallel to the x axis and three units below it.p is twice as far from q(6,2)as far from the origin.find the coordinates of p

Answer 1

the coordinates of p = (1.5 , - 3) ,  (- 5.5 , - 3)

Step-by-step explanation:

A point p lay on a line that is parallel to the x axis and three units below it

=> p = ( x , - 3)

p is twice as far from q(6,2) as from the origin

p Distance from origin = √(x - 0)² + (-3 - 0)²

= √(x² + 9)

p Distance from  q(6,2)  = √(x - 6)² + (-3 - 2)²

= √((x - 6)² + 25)

√((x - 6)² + 25) = 2√(x² + 9)

=> (x - 6)² + 25 = 4(x² + 9)

=> x² - 12x + 36 + 25 = 4x² + 36

=> 3x² + 12x - 25 = 0

=> x =( -12 ± √(12² - 4(3)(-25) )/6

=> x ≈ 1.5 , - 5.5

p = (1.5 , - 3)  , (- 5.5 , - 3)

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