What is the straight-line distance between (-2, -7) and (-4, -9) on a coordinate graph?
A. 2 sqrt2
B. 2 sqrt3
C. 2
D. 3
I think that it might be A or C but I'm unsure.
well, didn't you use your distance formula?
√(-4-(-2))^2+(-9-(-7))^2) = √((-2)^2+(-2)^2) = √(4+4) = √8 = 2√2
draw lines through the points in the x and y directions
find the right triangle whose hypotenuse is the distance you want
... the lengths of the sides are the distances between the two points in the x ... and y directions
you can also find the x and y distances by subtracting the corresponding coordinates of the points
(distance)^2 = (x-distance)^2 + (y-distance)^2
Aah, okay. Again, I was unsure of the process as this was a review question on a lesson I don't remember. Thank you.
To find the straight-line distance between two points on a coordinate graph, you need to apply the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two points are (-2, -7) and (-4, -9). These points form a right triangle, where the horizontal difference between the points represents one side of the triangle and the vertical difference represents the other side.
To find the horizontal difference, subtract the x-coordinates: -4 - (-2) = -4 + 2 = -2.
To find the vertical difference, subtract the y-coordinates: -9 - (-7) = -9 + 7 = -2.
Now, we have the horizontal difference (-2) and the vertical difference (-2). We can use these values to find the length of the hypotenuse, which is the straight-line distance between the two points.
Applying the Pythagorean theorem: hypotenuse^2 = horizontal difference^2 + vertical difference^2.
Let's substitute the values:
hypotenuse^2 = (-2)^2 + (-2)^2
= 4 + 4
= 8.
To determine the length of the hypotenuse, we need to take the square root of both sides:
hypotenuse = √8.
Simplifying the square root:
hypotenuse = √(4 * 2)
= √4 * √2
= 2√2.
The correct answer is A) 2√2, which represents the straight-line distance between the two given points on the coordinate graph.