Find the abscissa of the pointThe ordinate of a point is 6 and the distance from origin to the point is 9. Find the abscissa of the point.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We know that we can find the ordinate and the abscisa of a point, drawing perpendiculars from the given point to the x and y axis.

We'll form a right angle triangle, whose hypotenuse is the distance from origin to the point and cathetus is its abscisa.

We'll note the distance as r:

r = 9 units.

r^2 = 81 square units

We'll note the unknown abscisa as x and the ordinate as y.

y = 6 units

y^2 = 36 square units

We'll calculate x using Pythagorean Theorem:

r^2 = x^2 + y^2

x^2 = r^2 - y^2

x^2 = 81 - 36

x^2 = 45

x1 = sqrt 45

x1 = 3sqrt 5

x2 = - 3 sqrt 5

The ordinate of the point could be x = 3sqrt 5 or x  = -3sqrt 5.

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