What is the slope of the hypotenuses of the triangles in simplest form?

First-quadrant graph showing a ray through the origin and the points (2, 4), (3, 6), and (5, 10). Two triangles have their longest sides with endpoints along the line, one vertical leg, and one horizontal leg. The first triangle has a longest side with endpoints at (2, 4) and (3, 6). The second triangle has a longest side with endpoints at (5, 10) and (3, 6).

Question

What is the slope of the hypotenuses of the triangles in simplest form?
 
 
 
   First-quadrant graph showing a ray through the origin and the points (2, 4), (3, 6), and (5, 10). Two triangles have their longest sides with endpoints along the line, one vertical leg, and one horizontal leg. The first triangle has a longest side with endpoints at (2, 4) and (3, 6). The second triangle has a longest side with endpoints at (5, 10) and (3, 6).

anonymous · Answer

attachment

mrnood · Answer

the slope is worked out from the triangles and is the opposite/adjacent sides of the triangle

BOTH trinagles have the SAME slope (because they are on the the same straight line)

so for each triangle
 count the squares on the 'opposite' side (i.e. the vertical side)
count the squares on the 'adjacent' side (i.e. the horizontal side)

divide vertical by horizontal (opposite/adjacent = tan of angle)

that is the answer to the question


be sure you reduce it to its simplest form...