Coordinate Geometry

Question

Two points have coordinates A(3,1) and B(-1,5).Calculate the coordinates of P if P is on the x-axis and is equidistant from A and from B.If the figure APBQ is a rhombus,find the coordinates of Q.

Answer 1

P(x, 0)      Using the distance formula

 

√((x - 3)² + (0 - 1)²) = √((x + 1)² + (0 - 5)²)

(x - 3)² + 1 = (x + 1)² + 25

x² - 6x + 9 + 1 = x² + 2x + 1 + 25

-6x + 10 = 2x + 26

10 = 8x + 26

-16 = 8x

-2 = x

 

P(-2, 0)

 

Need the figure for the rhombus.