Question 752343
Q:
Point A is the origin. Find the coordinates of the two points that are 5 units distant from A, and have x-coordinates of +3. (Hint: Make a sketch. The two points fall on the line x={{{highlight(3)}}}, and therefore have coordinates ({{{highlight(3)}}},y) where y is unknown. Use the distance formula, suitably rearranged.)
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A: 
The distance between the origin and (3, y) is
{{{sqrt((y - 0)^2 + (3 - 0)^2)}}} = 5
{{{sqrt(y^2 + 9)}}} = 5, square both sides
{{{y^2 + 9}}} = 25
{{{y^2 }}} = 16, get the square root of both sides
y = ±4
The two points are (3,4) and (3,-4).