Points C and D are plotted on the coordinate plane as C(-3, 5) and D(1, -2). What is the exact distance between these two points?
To find the exact distance between two points, we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the values into the formula using the coordinates of the given points:
x1 = -3
y1 = 5
x2 = 1
y2 = -2
Now we can calculate the distance:
d = √((1 - (-3))^2 + (-2 - 5)^2)
= √((1 + 3)^2 + (-2 - 5)^2)
= √((4)^2 + (-7)^2)
= √(16 + 49)
= √65
Therefore, the exact distance between points C(-3, 5) and D(1, -2) is √65 units.
To find the exact distance between points C(-3, 5) and D(1, -2) on the coordinate plane, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be written as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d represents the distance between them.
In this case, x1 = -3, y1 = 5, x2 = 1, and y2 = -2.
Plugging these values into the distance formula:
d = sqrt((1 - (-3))^2 + (-2 - 5)^2)
= sqrt((1 + 3)^2 + (-2 - 5)^2)
= sqrt(4^2 + (-7)^2)
= sqrt(16 + 49)
= sqrt(65)
So, the exact distance between points C and D is sqrt(65).