Find the distance between point A(5, 3) and B(15, 10). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.(1 point)
The distance is about
units.
To find the distance between two points A(x1, y1) and B(x2, y2) in 2-dimensional space, you can use the distance formula which is derived from the Pythagorean theorem:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
For the points A(5, 3) and B(15, 10), you can plug in the coordinates into the formula:
Distance = √[(15 - 5)^2 + (10 - 3)^2]
Distance = √[(10)^2 + (7)^2]
Distance = √[100 + 49]
Distance = √149
Rounded to the nearest tenth, the distance is approximately:
Distance ≈ √149 ≈ 12.2
The distance between points A(5, 3) and B(15, 10) is about 12.2 units.
Find the distance between point M(−2, 9) and N(8, 12). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.(1 point)
The distance is about
units.
To find the distance between points M(-2, 9) and N(8, 12), we will use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
The coordinates for M are (x1, y1) = (-2, 9) and for N are (x2, y2) = (8, 12).
Let's plug these values into the formula:
Distance = √[(8 - (-2))^2 + (12 - 9)^2]
Distance = √[(8 + 2)^2 + (3)^2]
Distance = √[(10)^2 + (3)^2]
Distance = √[100 + 9]
Distance = √109
Rounded to the nearest tenth, the distance is approximately:
Distance ≈ √109 ≈ 10.4
The distance between points M(-2, 9) and N(8, 12) is about 10.4 units.
Find the distance between point C(5, 5) and D(8, 9). Round your answer to the nearest tenth. Click Here for Help Video. Click Here if you would like to create a visual.(1 point)
The distance is about
units.
To find the distance between points C(5, 5) and D(8, 9), we'll use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
The coordinates for C are (x1, y1) = (5, 5) and for D are (x2, y2) = (8, 9).
Let's plug these values into the formula:
Distance = √[(8 - 5)^2 + (9 - 5)^2]
Distance = √[(3)^2 + (4)^2]
Distance = √[9 + 16]
Distance = √25
The distance between points C and D is √25, which is:
Distance = 5
There's no need to round since 5 is an exact value.
The distance between points C(5, 5) and D(8, 9) is precisely 5 units.
To find the distance between two points in a plane, you can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, Point A has coordinates (x1, y1) = (5, 3) and Point B has coordinates (x2, y2) = (15, 10). Plugging these values into the distance formula, we get:
Distance = sqrt((15 - 5)^2 + (10 - 3)^2)
= sqrt(10^2 + 7^2)
= sqrt(100 + 49)
= sqrt(149)
≈ 12.2
Therefore, the distance between Point A and Point B is approximately 12.2 units (rounded to the nearest tenth).