Question

If the perpendicular distance of a point M from x-axis is 8 units and the foot of perpendicular lies on the y-axis, at a distance of 5 units from origin. Then, find all the possible coordinates of point M.​

Answer 1

Answer:

$| \sqrt[.0]{?} |$

Answer 2

If the perpendicular distance of a point M from y-axis is 8 units and the foot of perpendicular lies on the y-axis, at a distance of 5 units from origin then all the possible coordinates of point M are (±8 , ±5)

If the perpendicular distance of a point M from x-axis is 8 units and the foot of perpendicular lies on the x-axis, at a distance of 5 units from origin then all the possible coordinates of point M are (±5 , ±8)

Step 1:

Assume that point M is ( h , k)

Step 2:

Distance of point M (h , k) from x axis is given by

| k |

Step 3:

Equate the distance with given distance 8 unit

| k | = 8

Step 4:

Solve for values of k

k = ± 8

Step 5:

Foot of perpendicular of  M (h , k) on y axis is given by

(0 , k)    

Step 6:

Calculate distance of (0 , k) from origin and equate with 5  and solve for k

$\sqrt{(0-0)^2+(k-0)^2} =5$

$\sqrt{k^2} =5$

| k | = 5

k = ± 5

Value of k can not be 8 or 5 together hence mistake in data

Distance from x axis and distance of  foot of perpendicular on y axis from origin should be always Equal.

There is Mistake in data , Correct Question can be Either

If the perpendicular distance of a point M from y -axis is 8 units Then points   will be (±8 , ±5)

or

If the perpendicular distance of a point M from x -axis is 8 units the foot of perpendicular lies on the x-axis, at a distance of 5 units from origin Then points  will be (±5 , ±8)