Mathematics, 31.07.2019 00:30 ashlynm12

Methods of solving distance between two points

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The distance formula is an algebraic expression used to determine the distance between two points with the coordinates (x1, y1) and (x2, y2).

D=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√D=(x2−x1)2+(y2−y1)2

Example

Find the distance between (-1, 1) and (3, 4).

This problem is solved simply by plugging our x- and y-values into the distance formula:

D=(3−(−1))2+(4−1)2−−−−−−−−−−−−−−−−−−√=D=(3−(−1))2+(4−1)2==16+9−−−−−√=25−−√=5=16+9=25=5

Sometimes you need to find the point that is exactly between two other points. This middle point is called the "midpoint". By definition, a midpoint of a line segment is the point on that line segment that divides the segment in two congruent segments.

If the end points of a line segment is (x1, y1) and (x2, y2) then the midpoint of the line segment has the coordinates:

(x1+x22,y1+y22)(x1+x22,y1+y22)

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

step-by-step explanation:

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Methods of solving distance between two points...