To find the length between the two points, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two points form the endpoints of a straight line with a positive slope. We can consider this line as the hypotenuse of a right-angled triangle, with the vertical line segment (from -1 to 4) representing one side, and the horizontal line segment (from -2 to 2) representing the other side.
From the graph, we can see that the vertical line segment has a length of 4 - (-1) = 5 units, and the horizontal line segment has a length of 2 - (-2) = 4 units.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
Hypotenuse^2 = vertical side^2 + horizontal side^2
Hypotenuse^2 = 5^2 + 4^2
Hypotenuse^2 = 25 + 16
Hypotenuse^2 = 41
To find the length of the hypotenuse, we take the square root of both sides:
Hypotenuse = sqrt(41)
Rounding to the nearest hundredth, the length between the two points is approximately 6.40 units.
Use the image to answer the question.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
1 answer