Question

which of the following triangles would lie on the line graphed below? (with triangles and a coordinate grid)

Explanation:

Step1: Find the line's slope

The line passes through (0,0) and (10,0)? No, check intercepts: when x=10, y=0; when x=0, y=0? Wait, no—wait the grid: let's take two points: (0,0) and (5,4)? No, wait the line goes from (0,0) to (10, 8)? Wait no, the triangle sides: the left triangle has sides 4,6,? The right triangle has sides 4,2,? The middle 1,2,? Wait the line's slope: let's calculate slope m = rise/run. Suppose the line connects (0,0) to (5,4): m=4/5. Check triangle sides: for a triangle to lie on the line, its legs should have ratio equal to the slope (if right triangle with legs along axes direction). The left triangle: legs 4 and 6—ratio 4/6=2/3≠4/5. Middle: 1 and 2—ratio1/2≠4/5. Right triangle: legs 4 and 2—wait no, right triangle has legs 2 and 4? Wait the right triangle: sides 4 and 2—ratio 4/2=2? No, wait slope is y/x (if run is x, rise is y). Suppose the line has slope 2/5? No, wait the correct triangle: the rightmost triangle has legs 4 and 2? Wait no, the left triangle: 4 and 6—6/4=3/2; middle:1/2; right:2/4=1/2? No, wait the line: let's see the graph—when x=5, y=4? So slope is 4/5. Which triangle has legs in ratio 4:5? The left triangle: 4 and 6 no, right triangle: 4 and 2 no, middle:1 and 2 no? Wait wait, maybe the line is y = (2/5)x: when x=5, y=2. Then ratio 2/5. Right triangle: legs 2 and 5? No, right triangle has 4 and 2—2/4=1/2. Middle:1/2. Oh! The middle triangle: legs 1 and 2—ratio1/2; right triangle:2 and4—ratio1/2. Wait the line: let's check (10,5)? No, the line goes from (0,0) to (10,5)? Slope 5/10=1/2. Yes! So slope is 1/2. Which triangles have leg ratio 1/2? Middle triangle (1:2) and right triangle (2:4=1:2). Wait the right triangle: sides 4 and 2—if legs are 2 and4, ratio 2/4=1/2. So the right triangle (with sides 4 and2) has legs in slope ratio 1/2, so it lies on the line.

Answer:

The rightmost triangle (with sides 4 and 2)