Question
4 Find the distance between the two points: \( (-3,-4)(1,6) \). Round your answer to the nearest tenth.
Ask by Harrington Bolton. 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:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the given points:
d = √[(1 - (-3))² + (6 - (-4))²]
= √[(1 + 3)² + (6 + 4)²]
= √[(4)² + (10)²]
= √[16 + 100]
= √116
To round √116 to the nearest tenth, calculate:
√116 ≈ 10.8
Thus, the distance between the points is approximately 10.8 units.
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Simplify this solution Mind Expander
To find the distance between the points \((-3,-4)\) and \( (1,6) \), you can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the coordinates into the formula: \[ d = \sqrt{(1 - (-3))^2 + (6 - (-4))^2} \] \[ = \sqrt{(1 + 3)^2 + (6 + 4)^2} \] \[ = \sqrt{(4)^2 + (10)^2} \] \[ = \sqrt{16 + 100} \] \[ = \sqrt{116} \] Calculating this gives approximately: \[ d \approx 10.8 \] So, the distance between the two points is about 10.8 units when rounded to the nearest tenth.
