MathDB

A triangle with vertices as

A=(1,3)

B=(5,1)

, and

C=(4,4)

is plotted on a

6\times5

grid. What fraction of the grid is covered by the triangle?

<span class='latex-bold'>(A) </span>\frac{1}{6} \qquad <span class='latex-bold'>(B) </span>\frac{1}{5} \qquad <span class='latex-bold'>(C) </span>\frac{1}{4} \qquad <span class='latex-bold'>(D) </span>\frac{1}{3} \qquad <span class='latex-bold'>(E) </span>\frac{1}{2}

[asy]
draw((1,0)--(1,5),linewidth(.5)); draw((2,0)--(2,5),linewidth(.5)); draw((3,0)--(3,5),linewidth(.5)); draw((4,0)--(4,5),linewidth(.5)); draw((5,0)--(5,5),linewidth(.5)); draw((6,0)--(6,5),linewidth(.5)); draw((0,1)--(6,1),linewidth(.5)); draw((0,2)--(6,2),linewidth(.5)); draw((0,3)--(6,3),linewidth(.5)); draw((0,4)--(6,4),linewidth(.5)); draw((0,5)--(6,5),linewidth(.5)); draw((0,0)--(0,6),EndArrow); draw((0,0)--(7,0),EndArrow); draw((1,3)--(4,4)--(5,1)--cycle); label("

y

",(0,6),W); label("

x

",(7,0),S); label("

A

",(1,3),dir(230)); label("

B

",(5,1),SE); label("

C

",(4,4),dir(50)); [/asy]

Problem Statement