Question

The diagram shows a line joining O to P.
The gradient of the line is 2
The length of the line is √2645
Work out the coordinates of P.​

Answer 1

Answer: (23, 46)

Step-by-step explanation:

The equation of the line is y = 2x, and we can thus represent point P as (x, 2x)

Substituting into the distance formula,

$\sqrt{2645}=\sqrt{(x)^{2}+(2x)^{2}}\\\\2645=x^2 + (2x)^2\\\\2645=x^2 + 4x^2\\\\2645=5x^2\\\\529=x^2\\\\x=23$

Thus, the coordinates of P are (23, 46)