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2) What is the distance between points (-1, 3) and (5, -2)?

2) What is the distance between points (-1, 3) and (5, -2)?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Distance Between Points in a Coordinate Plane To calculate the distance between two points in a coordinate plane, you can use the Distance Formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here are a couple of examples: **2) What is the distance between points (-1, 3) and (5, -2)?** Using the Distance Formula: \[ x_1 = -1, \; y_1 = 3, \; x_2 = 5, \; y_2 = -2 \] \[ \text{Distance} = \sqrt{(5 - (-1))^2 + (-2 - 3)^2} \] \[ \text{Distance} = \sqrt{(5 + 1)^2 + (-2 - 3)^2} \] \[ \text{Distance} = \sqrt{6^2 + (-5)^2} \] \[ \text{Distance} = \sqrt{36 + 25} \] \[ \text{Distance} = \sqrt{61} \] \[ \text{Distance} = 7.81 \] Hence, the distance between the points (-1, 3) and (5, -2) is approximately 7.81 units. --- **3) What is the distance between points (0, -1) and (10, -5)?** Using the Distance Formula: \[ x_1 = 0, \; y_1 = -1, \; x_2 = 10, \; y_2 = -5 \] \[ \text{Distance} = \sqrt{(10 - 0)^2 + (-5 - (-1))^2} \] \[ \text{Distance} = \sqrt{10^2 + (-5 + 1)^2} \] \[ \text{Distance} = \sqrt{10^2 + (-4)^2} \] \[ \text{Distance} = \sqrt{100 + 16} \] \[ \text{Distance} = \sqrt{116} \] \[ \text{Distance} = 10.77 \] Hence, the distance between the points (0, -1) and (10, -5) is approximately 10.77 units. These examples demonstrate how to apply
Transcribed Image Text:### Distance Between Points in a Coordinate Plane To calculate the distance between two points in a coordinate plane, you can use the Distance Formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here are a couple of examples: **2) What is the distance between points (-1, 3) and (5, -2)?** Using the Distance Formula: \[ x_1 = -1, \; y_1 = 3, \; x_2 = 5, \; y_2 = -2 \] \[ \text{Distance} = \sqrt{(5 - (-1))^2 + (-2 - 3)^2} \] \[ \text{Distance} = \sqrt{(5 + 1)^2 + (-2 - 3)^2} \] \[ \text{Distance} = \sqrt{6^2 + (-5)^2} \] \[ \text{Distance} = \sqrt{36 + 25} \] \[ \text{Distance} = \sqrt{61} \] \[ \text{Distance} = 7.81 \] Hence, the distance between the points (-1, 3) and (5, -2) is approximately 7.81 units. --- **3) What is the distance between points (0, -1) and (10, -5)?** Using the Distance Formula: \[ x_1 = 0, \; y_1 = -1, \; x_2 = 10, \; y_2 = -5 \] \[ \text{Distance} = \sqrt{(10 - 0)^2 + (-5 - (-1))^2} \] \[ \text{Distance} = \sqrt{10^2 + (-5 + 1)^2} \] \[ \text{Distance} = \sqrt{10^2 + (-4)^2} \] \[ \text{Distance} = \sqrt{100 + 16} \] \[ \text{Distance} = \sqrt{116} \] \[ \text{Distance} = 10.77 \] Hence, the distance between the points (0, -1) and (10, -5) is approximately 10.77 units. These examples demonstrate how to apply
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