grewalss
Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Find the shortest distance between the line y = 2x + 3 and the point (-5, 8)
PLEASE EXPLAIN IT

Sagot :

Answer:

6.7 units

Step-by-step explanation:

The shortest distance between two lines is the perpendicular line.

y = 2x + 3

Slope of the perpendicular line: - 1/2

Point (-5,8)

b (y-intersect) = 8 - (-1/2)(-5) = 11/2

Perpendicular line equation: y = -1/2x + 11/2

y = y

2x +3 = -1/2x + 11/2

2x + 1/2x = 11/12 - 3

5/2x = 5/2

x = (5/2) / (5/2)

x = 1

Plug x = 1 into any of the equations of the line to find y.

y = 2x + 3

y = (2*1)+3 = 5

Points from the perpendicular line (1,5) and (-5,8)

Distance between these two points:

d = sqrt[(-5-1)^2 + (8-5)^2]

= sqrt (6^2 + 3^2) = sqrt 45

= 6.7

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.