Question
4 Find the distance between the two points: \( (-3,-4)(1,6) \). Round your answer to the nearest tenth.
Ask by Jimenez Black. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The distance between the points (-3, -4) and (1, 6) is approximately 10.8 units.
Solution
To find the distance between the points (-3, -4) and (1, 6), use the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Plug in the coordinates:
x₁ = -3, y₁ = -4
x₂ = 1, y₂ = 6
Calculate the differences:
x₂ - x₁ = 1 - (-3) = 4
y₂ - y₁ = 6 - (-4) = 10
Now, substitute these values into the formula:
Distance = √[(4)² + (10)²]
= √[16 + 100]
= √116
To obtain a decimal approximation, √116 ≈ 10.7703, which rounds to 10.8 (to the nearest tenth).
Thus, the distance between the points is approximately 10.8.
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Simplify this solution The Deep Dive
To find the distance between the two points \((-3,-4)\) and \((1,6)\), we can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \((x_1, y_1) = (-3, -4)\) and \((x_2, y_2) = (1, 6)\). Plugging in these values, we get: \[ d = \sqrt{(1 - (-3))^2 + (6 - (-4))^2} \] This simplifies to: \[ d = \sqrt{(1 + 3)^2 + (6 + 4)^2} = \sqrt{(4)^2 + (10)^2} = \sqrt{16 + 100} = \sqrt{116} \] Calculating the square root gives us approximately \(10.8\). Therefore, the distance between the two points is approximately \(10.8\) when rounded to the nearest tenth.
