1. Find the distance between the pair of points. Round to the nearest tenth is necessary. (-10, 4) and (6, 12)
a. 11.4
b. 17.9
c. 31.4
d. 23.7
2. Find the distance between the pair of points. Round to the nearest tenth, if necessary. (-8,10) and (-2,10)
a. 13.6
b. 21.2
c. 23.4
d. 6.0
Please just explain how to do this. Thank you!
(-10, 4) and (6, 12)
distance is hypotenuse of right triangle
d^2 = (X2-X1)^2 + (Y2-Y1)^2
d^2 = (6-(-10)^2 + (12-4)^2
d^2 = 16^2 + 8^2
d^2 = 256 + 64
d^2 = 320
d = sqrt(320) = 17.89
(4,-5), (-3,-3)
To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is represented as:
d = √((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.
Let's use this formula to solve the given problems.
1. Distance between (-10, 4) and (6, 12):
Using the distance formula, let's substitute the given coordinates into the equation:
d = √((6 - (-10))^2 + (12 - 4)^2)
d = √((16)^2 + (8)^2)
d = √(256 + 64)
d = √320
d ≈ 17.9
Therefore, the distance between the given points is approximately 17.9.
So, the correct answer is (b) 17.9.
2. Distance between (-8, 10) and (-2, 10):
Similarly, let's substitute the given coordinates into the distance formula:
d = √((-2 - (-8))^2 + (10 - 10)^2)
d = √((6)^2 + (0)^2)
d = √(36 + 0)
d = √36
d = 6.0
Therefore, the distance between the given points is 6.0.
So, the correct answer is (d) 6.0.