# Find the coordinates

Construct the quadrature of 3 squares. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3). Let b = 4 be a line segment that extends along the x-axis from the origin O to the point A at (4,0). Let x be the hypotenuse of triangle ABO.

Let c = 2 be a line segment extending above the x-axis from point A to a point C, forming a right angle at CAB. Let d be the hypotenuse from C to B. Draw a perpendicular line to the x-axis from C that is called D.

1. Show that Triangle ABO is similar to Triangle CAD, where O is the origin.

2. Find the coordinates of C in terms of a and b.

3. Use the distance formula to find the distance of BC.

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#### Solution Preview

Construct the quadrature of 3 squres. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3). Let b = 4 be a line segment that extends along the x-axis from the origin O to the point A at (4,0). Let x be the hypotenus of Triangle ABO.

Let c = 2 be a line segment extending above the x-axis ...

#### Solution Summary

This posting helps with geometry problems. It helps show a triangle is similar to another and helps find coordinates.