Question

M is the foot of the perpendicular from point A to the X-axis. M lies on the negative direction of the X-axis and AM = 8 units. The coordinates of A could be:


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Answer 1

Given: M is the foot of the perpendicular from point A to the X-axis. M lies on the negative direction of the X-axis and AM = 8 units.

To find: The coordinates of A.

Solution:

According to the question, AM is a straight line constructed on the x-axis. Since M lies in the negative direction of the x-axis, the coordinates of A will also have a negative value of x. As the length of AM is 8 units, this means that the y-coordinate is 8. Hence, the coordinates of a can be written as follows.

$A = (-x,8)$

Therefore, the coordinates of A could be (-x,8)

Answer 2

M is the foot of the perpendicular from point A to the X-axis. M lies on the negative direction of the X-axis and AM = 8 units. The coordinates of A could be (-x , ±8)

Assume that coordinate of point A is (-x , y)   where x > 0 as perpendicular from point A lies on the negative direction of the X-axis.

Foot of the perpendicular from point A (-x, y) to the X-axis will be M ( -x , 0)

Distance between A and M   is  $\sqrt{(-x-(-x))^2+(y-0)^2}$

Distance between A and M is given as 8 units

Equate Distance

$\sqrt{(-x-(-x))^2+(y-0)^2}=8$

$\sqrt{0+ y ^2}=8$

$\sqrt{ y ^2}=8$

| y | = 8

y = ±8

The coordinates of A could be (-x , ±8) where x >0

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