Find the coordinates of the points that are units away from the origin and have an x-coordinate equal to .

Question

Find the coordinates of the points that are  units away from the origin and have an x-coordinate equal to  .

Quizplus · Accepted Answer

We know that the point is on the x-axis and the x-coordinate is 11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11 . The distance of the point from the origin is 11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11 units.

Let the y-coordinate of the point be y. 
Using the distance formula, we can set up an equation:

sqrt((11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11)^2 + y^2) = 11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11

Solving for y:

(11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11)^2 - (11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11)^2 = y^2 
y = +/- sqrt((11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11)^2 - (11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11)^2)

Since the point is on the x-axis, the y-coordinate is either 0 or +/- sqrt((11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11)^2 - (11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11)^2).

Using a calculator or simplifying the expression, we find that the y-coordinates are approximately equal to 11eaa8b1_dcda_8f0d_b1b6_11c9fd5601d2_TB6026_11 and -11eaa8b1_dcda_8f0d_b1b6_11c9fd5601d2_TB6026_11.

Therefore, the two points that are 11eaa8b1_dcda_19d8_b1b6_b93b2fd450af_TB6026_11 units away from the origin and have an x-coordinate equal to 11eaa8b1_dcda_40e9_b1b6_5b39254a0269_TB6026_11 are:

11eaa8b1_dcda_67fc_b1b6_9d48ebe03840_TB6026_11 and 11eaa8b1_dcda_8f0d_b1b6_11c9fd5601d2_TB6026_11

Find the Coordinates of the Points That Are Units