Find the slope of a line a. parallel and b. perpendicular to the line x+2y=2.

capellitad9
2022-07-25
Answered

Find the slope of a line a. parallel and b. perpendicular to the line x+2y=2.

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suchonos6r

Answered 2022-07-26
Author has **14** answers

line $x+2y=2\phantom{\rule{0ex}{0ex}}2y=-x+2\phantom{\rule{0ex}{0ex}}y=-\frac{1}{2}x+2$

a. Parallel $m=-\frac{1}{2}$

b. Perpendicular ${m}_{1}{m}_{2}=-1\phantom{\rule{0ex}{0ex}}{m}_{2}=2;\text{}{m}_{1}=-\frac{1}{2}$

a. Parallel $m=-\frac{1}{2}$

b. Perpendicular ${m}_{1}{m}_{2}=-1\phantom{\rule{0ex}{0ex}}{m}_{2}=2;\text{}{m}_{1}=-\frac{1}{2}$

asked 2022-07-08

Let us start with these two equations of two lines:

$x+y=4$

$x-y=2$

They intersect at $(x,y)=(3,1)$

Let us now translate (move) both lines so that they intersect at (0, 0). We need to move both lines by -3 along x-axis and by -1 along y-axis. So the equations of the lines become.

$(x+3)+(y+1)=4$

$(x+3)-(y+1)=2$

This is equivalent to

$x+y=0$

$x-y=0$

Why do the RHS become 0 for both equations? This happens no matter which two intersecting lines we begin with. What is the geometrical interpretation of this?

$x+y=4$

$x-y=2$

They intersect at $(x,y)=(3,1)$

Let us now translate (move) both lines so that they intersect at (0, 0). We need to move both lines by -3 along x-axis and by -1 along y-axis. So the equations of the lines become.

$(x+3)+(y+1)=4$

$(x+3)-(y+1)=2$

This is equivalent to

$x+y=0$

$x-y=0$

Why do the RHS become 0 for both equations? This happens no matter which two intersecting lines we begin with. What is the geometrical interpretation of this?

asked 2022-11-12

The length of a rectangle is 14 m longer than its width and the area of the rectangle is 400 m2. Find the exact dimensions of the rectangle: width and length.

asked 2021-12-13

Let $Q}^{2$ be the rational plane of all ordered pairs (x,y) of rational numbers with the usual interpretations of the undefined geometric terms used in analytical geometry. Show that axiom C-1 and the elementary continuity principle fail in $Q}^{2$ . (Hint: the segment from (0,0) to (1,1) can not be laid off on the x axis from the origin.

Axiom C-1: If A, B are two points on a line a, and if A' is a point upon the same or another line a′ , then, upon a given side of A′ on the straight line a′ , we can always find a point B′ so that the segment AB is congruent to the segment A′B′ . We indicate this relation by writing$AB\stackrel{\sim}{=}A\prime B\prime$ . Every segment is congruent to itself; that is, we always have $AB\stackrel{\sim}{=}AB$ .

Axiom C-1: If A, B are two points on a line a, and if A' is a point upon the same or another line a′ , then, upon a given side of A′ on the straight line a′ , we can always find a point B′ so that the segment AB is congruent to the segment A′B′ . We indicate this relation by writing

asked 2022-06-23

Equation of the ellipse between 2 points (its vertices)

Start point and end point:

$A(x,y)\phantom{\rule{1em}{0ex}}B(x,y)$

Ellipse width:

$w=2.5$

Midpoint or center of the ellipse:

$M=(\frac{{A}_{x}+{B}_{x}}{2},\frac{{A}_{y}+{B}_{y}}{2})$

The angle (that would be the angle between points A and B):

$\theta =?$

Parametric equation of the ellipse with rotation:

$x=a\ast cos(t)\ast cos(\theta )+b\ast sin(t)\ast sin(\theta )$

$y=b\ast sin(t)\ast cos(\theta )-a\ast cos(t)\ast sin(\theta )$

Start point and end point:

$A(x,y)\phantom{\rule{1em}{0ex}}B(x,y)$

Ellipse width:

$w=2.5$

Midpoint or center of the ellipse:

$M=(\frac{{A}_{x}+{B}_{x}}{2},\frac{{A}_{y}+{B}_{y}}{2})$

The angle (that would be the angle between points A and B):

$\theta =?$

Parametric equation of the ellipse with rotation:

$x=a\ast cos(t)\ast cos(\theta )+b\ast sin(t)\ast sin(\theta )$

$y=b\ast sin(t)\ast cos(\theta )-a\ast cos(t)\ast sin(\theta )$

asked 2021-12-18

When is a rectangle a regular polygon?

asked 2021-12-12

In the diagram below, a circle with centre O is given with diameter AB. The coordinates of A and B are (4 ; 4) and (2 ; -6) respectively. ya A(4; 4) B(2; -6)

a) Determine the coordinates of O, the centre of the circle.

b) Calculate the length of the radius of the circle.

c) Write down the equation of the circle in form:

$(x-a)}^{2}+{(y-b)}^{2}={r}^{2$

d) Write down the equation of the circle in form:

$a{x}^{2}+bx+c{y}^{2}+dy+e=0$

a) Determine the coordinates of O, the centre of the circle.

b) Calculate the length of the radius of the circle.

c) Write down the equation of the circle in form:

d) Write down the equation of the circle in form:

asked 2021-11-26

What is EG?