we know that In a right triangle there are two legs and one hypotenuse step 1 find the distance AB d=√[(y2-y1)²+(x2-x1)²]------> d=√[(4-4)²+(6-1)²]-----> d=√25----> 5 AB=5 units
step 2 find the distance BC d=√[(y2-y1)²+(x2-x1)²]------> d=√[(1-4)²+(6-6)²]-----> d=√9----> 3 BC=3 units
step 3 find the distance AC d=√[(y2-y1)²+(x2-x1)²]------> d=√[(1-4)²+(6-1)²]-----> d=√34----> 5.83 AC=5.83 units
therefore the two legs are AB=5 units BC=3 units the hypotenuse is AC=5.83 units
the answer is the length of the longer leg is AB=5 units
