Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points, to the nearest tenth (if necessary).
left bracket, 4, comma, 7, right bracket, and , left bracket, minus, 5, comma, minus, 5, right bracket
(4,7) and (−5,−5)
Leg 1: __, Leg 2: __, Distance: __
To graph the right triangle, plot the points (4,7) and (-5,-5) on a coordinate plane:
(4,7) is on the upper right side and (-5,-5) is on the bottom left side.
Next, connect the two points to form the hypotenuse of the triangle.
To find the length of the legs and the distance between the two points, we can use the distance formula:
Distance = √((x2-x1)^2 + (y2-y1)^2)
For leg 1, between points (4,7) and (-5,7), the distance is:
Leg 1 = √((-5-4)^2 + (-5-7)^2) = √((-9)^2 + (-12)^2) = √(81 + 144) = √225 = 15
For leg 2, between points (-5,7) and (-5,-5), the distance is:
Leg 2 = √((-5--5)^2 + (-5-7)^2) = √(0^2 + (-12)^2) = √144 = 12
The distance between the two points is the length of the hypotenuse of the triangle.
Distance = √((4-(-5))^2 + (7-(-5))^2) = √(9^2 + 12^2) = √(81 + 144) = √225 = 15
So, the lengths of the legs are Leg 1 = 15 and Leg 2 = 12, and the distance between the two points is 15.