In the square grid shown, what is tan∠AOB?
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Step-by-Step Solution
Step 1: Identify Coordinates
We can set the origin O at (0,0) on the coordinate plane. By observing the grid, point A is located at (1,4) and point B is located at (4,1). Each square in the grid represents one unit.
Step 2: Calculate Slopes
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by m=x2−x1y2−y1. We calculate the slopes of lines OA and OB.
Step 3: Apply Tangent Formula
The tangent of the angle θ between two lines with slopes m1 and m2 is given by the formula tanθ=1+m1m2m1−m2. Here, m1=mOA and m2=mOB.
Step 4: Substitute and Calculate
Substitute the calculated slopes into the formula. Simplify the expression to find the value of tan∠AOB.