The vertices of a rectangle are at (−4, 2), (3, 2), (3, −2), and (−4, −2).
What is the length of the longer side of the rectangle?
3 - -4 = ?
To find the length of the longer side of the rectangle, we need to calculate the distance between two consecutive vertices of the rectangle. We can use the distance formula to find the distance between two points in a Cartesian coordinate system.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between the two consecutive vertices (-4, 2) and (3, 2):
d1 = sqrt((3 - (-4))^2 + (2 - 2)^2)
= sqrt((7)^2 + (0)^2)
= sqrt(49 + 0)
= sqrt(49)
= 7
Now, let's calculate the distance between the other two vertices (3, -2) and (-4, -2):
d2 = sqrt((-4 - 3)^2 + (-2 - (-2))^2)
= sqrt((-7)^2 + (0)^2)
= sqrt(49 + 0)
= sqrt(49)
= 7
Since both distances are the same, the longer side of the rectangle is 7 units.