Online Notes and Lectures: distance

Showing posts with label distance. Show all posts

Tuesday, December 31, 2013

Find the relation between x and y, if the point (x, y) is equidistant from (7, -6),(-3, 4)

0 comments Posted by Anonymous at 4:18 PM

Hits:

Problem: How to Find the relation between x and y, if the point (x, y)is equidistant from (7, -6),(-3, 4).

$(7,-6),(-3,4)\,$

Solutions:

Find the distance between (x,y) and the first point is

$\sqrt{(x-7)^2+(y+6)^2}\,$

$\sqrt{x^2+49-14x+y^2+36+12y}\,$

$\sqrt{x^2+y^2-14x+12y+85}\,$

Let this expression be 1.

Find the distance between (x,y) and the second point is

$\sqrt{(x+3)^2+(y-4)^2}\,$

$\sqrt{x^2+9+6x+y^2+16-8y}\,$

$\sqrt{x^2+y^2+6x-8y+25}\,$

Let this expression be 2.

As per the given condition,equating both the expressions,

$\sqrt{x^2+y^2-14x-12y+85}=\sqrt{x^2+y^2+6x-8y+25}\,$

Squaring on both sides,we get

$x^2+y^2-14x+12y+22=x^2+y^2+6x-8y+25\,$

cancelling the terms which are common on both sides,

$-14x-6x+12y+8y=-60\,$

$-20x+20y=-60\,$

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.

Tags: distance, Geometry Problems

Find the value of a if the distance between the points (a, 2),(3, 4) is 2

0 comments Posted by Anonymous at 3:34 PM

Hits:

Problem: How to find the value of a if the distance between the points (a, 2),(3, 4) is 2.

$(a,2),(3,4)\,$

Solutions:

The distance between the given points is

$\sqrt{(a-3)^2+(2-4)^2}=2\,$

Simplifying

$\sqrt{a^2+9-6a+4}=2\,$

Squaring on both sides,

$a^2-6a+13=4\,$

$a^2-6a+9=0\,$

$(a-3)^2=0\,$

Finally, the value of a is 3.

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.

Tags: distance, Geometry Problems

Saturday, December 28, 2013

Given (0, 9) and (6, -9), find the midpoint, distance, slope, and equation of the line.

0 comments Posted by Anonymous at 11:12 PM

Hits:

Problem: Given these pairs of points, (0, 9)) and (6, -9), find the midpoint, distance, slope, and equation of the line.

$(0,9),(6,-9)\,$

Solutions:

To find the midpoint, average the x coordinates and y coordinates. The midpoint is

$\left(\frac{0+6}{2},\frac{9-9}{2}\right) = (3,0)\,$

To find the (always zero or positive) distance, use the formula

$d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,$

$d = \sqrt{(6)^2+(-9-9)^2} = \sqrt{36+18^2} = \sqrt{(2\cdot 3)^2+(2\cdot 3^2)^2} = \sqrt{(2\cdot 3)^2(1+3^2} = 6\sqrt{10}\,$

To find the slope, use the formula

$m = \frac{y_2-y_1}{x_2-x_1}\,$

$m = \frac{-9-9}{6-0} = -3\,$

The equations of the line are

Method 1:

$y=mx+b\,$

Plug in one known point (say, (0, 9)) and the calculated slope.

$9 = -3\cdot 0 + b\,$

$b = 9\,$

Now plug b and m into the line equation:
$y = -3x + 9\,$

Method 2:

$(y-y_1) = m(x-x_1)\,$

Plug in one known point (say, (6, –9) ) and the calculated slope.

$(y+9) = -3(x-6)\,$

$y = -3x + 18 - 9\,$

$y = -3x + 9\,$

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.

Tags: distance, equation of line, Geometry Problems, midpoint, slope

Given (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

0 comments Posted by Anonymous at 10:55 PM

Hits:

Problem: Given these pairs of points, (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

$(-5,15),(-5,9)\,$

Solutions:

To find the midpoint, average the x coordinates and y coordinates. The midpoint is

$\left(\frac{-5-5}{2},\frac{15+9}{2}\right) = \left(-5,\frac{15+9}{2}\right) = \left(-5,\frac{15+9}{2}\right)\,$

To find the (always zero or positive) distance, use the formula

$d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,$

$d = \sqrt{(-5+5)^2+(15-9)^2} = \sqrt{0^2+6^2} = \sqrt{6^2} = 6\,$

To find the slope, use the formula

$m = \frac{y_2-y_1}{x_2-x_1}\,$

$m = \frac{9-15}{-5-(-5)} = undefined\,$ (which means it is a vertical line, which has infinite slope)

Since the line is vertical, there is only one x value that will give all y values. The equation for the line is

$x = -5\,$

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.

Tags: distance, equation of line, Geometry Problems, midpoint, slope

Given (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

0 comments Posted by Anonymous at 10:33 PM

Hits:

Problem: Given these pairs of points, (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

$(4,13),(09,0)\,$

Solutions:

To find the midpoint, average the x coordinates and y coordinates. The midpoint is

$\left(\frac{4+0}{2},\frac{13+9}{2}\right) = (2,11),$

To find the (always zero or positive) distance, use the formula

$d = +\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}\,$

$d = \sqrt{(4-0)^2+(13-9)^2} = \sqrt{(4)^2+4^2} = \sqrt{16+16} = \sqrt{16*2} = \sqrt{4*4*2} = 4\sqrt{2}\,$

To find the slope, use the formula

$m = \frac{y_2-y_1}{x_2-x_1}\,$

$m = \frac{9-13}{0-4} = \frac{-4}{-4} = 1,$

The equations of the line are

Method 1:

$y=mx+b\,$

Plug in one known point (say, (0, 9)) and the calculated slope.

$9 = 0 + b\,$

$b = 9\,$

Now plug b and m into the line equation:

$y = x + 9\,$

Method 2:

$(y-y_1) = m(x-x_1)\,$

Plug in one known point (say, (4, 13)) and the calculated slope.

$(y-13) = (x-4)\,$

$y = x + 9\,$

$y = x + 9\,$

List of Similar Problems with Complete Solutions

NOTE:

For any Questions, Clarifications and any violent Reactions use the comment section below. I'll be much willing to assist you.

Tags: distance, equation of line, Geometry Problems, midpoint, slope

Visit: The New Homepage

Tuesday, December 31, 2013

Find the relation between x and y, if the point (x, y) is equidistant from (7, -6),(-3, 4)

Problem: How to Find the relation between x and y, if the point (x, y)is equidistant from (7, -6),(-3, 4).

Solutions:

List of Similar Problems with Complete Solutions

NOTE:

Find the value of a if the distance between the points (a, 2),(3, 4) is 2

Problem: How to find the value of a if the distance between the points (a, 2),(3, 4) is 2.

Solutions:

Simplifying

List of Similar Problems with Complete Solutions

NOTE:

Saturday, December 28, 2013

Given (0, 9) and (6, -9), find the midpoint, distance, slope, and equation of the line.

Problem: Given these pairs of points, (0, 9)) and (6, -9), find the midpoint, distance, slope, and equation of the line.

Solutions:

List of Similar Problems with Complete Solutions

NOTE:

Given (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

Problem: Given these pairs of points, (-5, 15) and (-5, 9), find the midpoint, distance, slope, and equation of the line.

Solutions:

List of Similar Problems with Complete Solutions

NOTE:

Given (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

Problem: Given these pairs of points, (4, 13) and (0, 9), find the midpoint, distance, slope, and equation of the line.

Solutions:

List of Similar Problems with Complete Solutions

NOTE:

PinoyBIX Latest Update

Subscribe Here

Share this page

Note Navigator