/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 66 Find the midpoint of each segmen... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 66

Find the midpoint of each segment with the given endpoints. $$ (-10,4) \text { and }(7,1) $$

Short Answer

Expert verified
The midpoint is \left( -1.5, 2.5 \right).

Step by step solution

01

Understand the Midpoint Formula

The midpoint of a segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) can be found using the formula: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \] where \( M \) is the midpoint.
02

Plug in the Coordinates

Substitute the given coordinates \( (-10, 4) \) and \( (7, 1) \) into the midpoint formula.For \((x_1, y_1) = (-10, 4)\) and \((x_2, y_2) = (7, 1)\), we have: \[ M = \left( \frac{-10 + 7}{2}, \frac{4 + 1}{2} \right) \]
03

Calculate the Midpoint

Now, compute the values inside the formula: \[ M = \left( \frac{-3}{2}, \frac{5}{2} \right) \] Simplify further: \[ M = \left( -1.5, 2.5 \right) \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coordinate Geometry
Coordinate geometry is a branch of geometry where the position of points on a plane is described using an ordered pair of numbers, typically \((x, y)\). A key concept in coordinate geometry is understanding how to find the location of certain points, such as midpoints, between others. This involves using formulas to mathematically determine distances and positions. Learning these techniques is crucial for solving various geometric problems on the coordinate plane effectively.
Algebra
Algebra provides the tools needed to manipulate mathematical expressions and equations. When dealing with coordinate geometry problems like midpoint calculation, algebraic skills become essential. You use algebra to substitute given values into the formula and then simplify those expressions. For instance, knowing how to handle addition, division, and understanding how to simplify fractions are all fundamental algebraic skills used in the provided example.
Midpoint Calculation
The midpoint calculation helps you find the point that is exactly in between two other points. Using the midpoint formula \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \], you can determine this point by adding the corresponding coordinates of the given points and then dividing by 2.

For example, given endpoints \((-10, 4) \) and \(7, 1)\), you would substitute these into the formula, yielding:
  • \( x \text{ component: } \frac{-10 + 7}{2} = -1.5\)
  • \( y \text{ component: } \frac{4 + 1}{2} = 2.5\)

Hence, the midpoint is \(-1.5, 2.5\). This method provides a straightforward way to pinpoint exactly where the middle of a segment lies on the coordinate plane.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Graph each linear or constant function. Give the domain and range. $$ f(x)=-x $$

Graph each line passing through the given point and having the given slope. (-3,1)\(;\) undefined slope

Graph each linear or constant function. Give the domain and range. $$ f(x)=-2.5 $$

A taxicab driver charges \(\$ 2.50\) per mile. (a) Fill in the table with the correct response for the price \(f(x)\) the driver charges for a trip of \(x\) miles. (b) The linear function that gives a rule for the amount charged is \(f(x)=\) (c) Graph this function for the domain \\{0,1,2,3\\} using the set of axes at the right. $$ \begin{array}{c|c} x & f(x) \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline \end{array} $$

Determine whether each pair of lines is parallel, perpendicular, or neither. \(4 x+y=0\) and \(5 x-8=2 y\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.