### Midpoint Calculation Problem#### Problem Statement:Line segment $ \overline{XY} $ has an endpoint $ X $ at $(2, -4)$. If the midpoint of $ \overline{XY} $ is $(-3, -1)$, what are the coordinates of $ Y $?**Solution Box:** $ Y: \_\_\_\_\_\_\_\_\_\_\_\_ $#### Explanation of the Problem:This problem involves finding the coordinates of the other endpoint $ Y $ of a line segment when one endpoint $ X $ and the midpoint are given. The coordinates of $ X $ are $(2, -4)$, and the coordinates of the midpoint are $(-3, -1)$.#### Steps to Solve:1. **Understand the Midpoint Formula:** The midpoint $(M)$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by: \[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]2. **Set Up the Equation:** Given the midpoint $(-3, -1)$ and one endpoint $ X(2, -4) $, set up the equations for the x and y coordinates of the midpoint.3. **Solve for $ x_2 $ and $ y_2 $ (coordinates of $ Y $):** \[ \left( \frac{2 + x_2}{2}, \frac{-4 + y_2}{2} \right) = (-3, -1) \] Equate the x-coordinates: \[ \frac{2 + x_2}{2} = -3 \\ 2 + x_2 = -6 \\ x_2 = -6 - 2 \\ x_2 = -8 \] Equate the y-coordinates: \[ \frac{-4 + y_2}{2} = -1 \\ -4 + y_2 = -2 \\ y_2 = -2 + 4 \\ y_2 = 2 \]4. **

The midpoint of two points and is given by: where are coordinates of the midpoint.

Answered: 2. XY has an endpoint X at (2,– 4). If…

Math

Geometry

2. XY has an endpoint X at (2,– 4). If the midpoint of XY is (– 3,– 1), what are the coordinates of Y? Y:

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

See similar textbooks

Related questions

Q: Q2. Solve the following questions. (.. (a) Find the value of k, if the points A(2, 3), B(4, k) and…

Q: Let j=8 k=3 let A (0, 7-k), B(6, -k+5). Find all points P on the line y = 9-k such that AP I BP.

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Specify m to distance from point M (1;0) to the lines (Δ):4x+3y+m= 0 by 2.

A: Please see the below picture for detailed solution.

Q: The real part of (11x + 1 + iy)dz where C is the line joining 1- i to 2+ i is Answer:

Q: 22.) Determine if the graph of the relations below are symmetric w/ respect to a) the x-axis, b.)…

A: Given:The functions are:a) b) c) Aim:To check whether the functions are symmetric abouta) the…

Q: 20b. Find the coordinates of A' after A(-3, 4) has been reflected: Reflection in the x-axis: A'= I…

A: To find the reflections

Q: Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed…

Q: Which of the following points is inside the circle whose equation is (x – 8)? + (y – 5)² = 36 (3,11)…

A: We have to check which points is inside the circle whose equation is (x - 8)2 + (y - 5)2 = 36 Let ,…

Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

Q: iven two line segments, construct a rhombus whose diagonals have lengths equal to the lengths of the…

Q: . (a) Let C be the line segment from a point (a, b) to a point (c, d). Show that -ydx + xdy = ad –…

A: It is given that, C is the line segment from a point a,b to a point c,d. Now, combining it with…

Q: . Find the coordinates of if M is the midpoint of and M(2,-1).

Q: point

A: Please refer to the image below

Q: 6. The picture is aligned with the coordinate axes such that point D is at the origin (0,0) and…

Q: .What is the set of points given by (a) x² + 2xy + y² = 1 (b) x² + y² - 2x + 4y + 5 = 0?

A: To find the set of points satisfying the given relation.

Q: A(2, 0) and B(0, 7) are points on the x- and y-axes, respectively. Find the coordinates of point…

Q: Find the line of intersection between the lines: +1 and +.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

Q: Let P(-4, 1, -3) be a point that is not on the line L . Let the line L pass-through points Q and R…

Q: 3. Plot each of the points below and give their coordinates in the specified coordinate system. a.…

Q: Let P be a point not on the line L that passes through the points Q and R. The distance d from the…

Question

### Midpoint Calculation Problem

#### Problem Statement:
Line segment $ \overline{XY} $ has an endpoint $ X $ at $(2, -4)$. If the midpoint of $ \overline{XY} $ is $(-3, -1)$, what are the coordinates of $ Y $?

**Solution Box:**
$ Y: \_\_\_\_\_\_\_\_\_\_\_\_ $

#### Explanation of the Problem:

This problem involves finding the coordinates of the other endpoint $ Y $ of a line segment when one endpoint $ X $ and the midpoint are given. The coordinates of $ X $ are $(2, -4)$, and the coordinates of the midpoint are $(-3, -1)$.

#### Steps to Solve:

1. **Understand the Midpoint Formula:**
The midpoint $(M)$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

2. **Set Up the Equation:**
Given the midpoint $(-3, -1)$ and one endpoint $ X(2, -4) $, set up the equations for the x and y coordinates of the midpoint.

3. **Solve for $ x_2 $ and $ y_2 $ (coordinates of $ Y $):**
\[
\left( \frac{2 + x_2}{2}, \frac{-4 + y_2}{2} \right) = (-3, -1)
\]

Equate the x-coordinates:
\[
\frac{2 + x_2}{2} = -3 \\
2 + x_2 = -6 \\
x_2 = -6 - 2 \\
x_2 = -8
\]

Equate the y-coordinates:
\[
\frac{-4 + y_2}{2} = -1 \\
-4 + y_2 = -2 \\
y_2 = -2 + 4 \\
y_2 = 2
\]

4. **

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Implicit Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

F: #8.
3. Solve for y: - 5 ( 2x - 7) > 3 4. Solve for z: |z - 7| < 2 5. For the following points find the midpoint and the distance between the two points in the coordinate plane. A (-3, 4) and B (5, 7)
The 3 lines x = 3, y – 2.5 = --(x – 0.5), and y – 2.5 = x – 3.5 intersect at point P. Find the coordinates of P. Verify algebraically that the lines all intersect at P. Point P = (
Find beR so that | 4a" dy – 2zy dz = 145, Where C is the segment (1, –5) a (-2, –3), followed by the part y =1-x² x = -2 a x = 2,followed by the segment of (2, -3) а (4, 5). Choose an alternative: a. None of the alternatives b. 1 с. —5 d. –3 e. 2 f. 0
The question is attached below:
Consider the line segment joining A(−3, 3) and B(9, 7). (a) Find an equation, in the form of Ax + By = C, that expresses the fact that a point P(x, y) is equidistant from A and from B.
14