Math homework help please. (Geometry)?

Question

Question 1 : How do you determinate the DISTANCE between two points on a coordinate plane??

Question 2: How do you determinate the MIDPOINT between two pounts on a coordinate plane?

Answer 1

First, a little english...there is no such word as determinate.  The strategy is:  how do you determine...?

Distance on the coordinate plane is calculated by using the Pythagorean Theorem:  d = sqrt((x1 -x2)^2 + (y1 -y2)^2)

where the two points are given by:  (x1,y1) and (x2,y2)

The midpoint of a line segment is determined by finding the average of the x-coordinates and the average of the y-coordinates.  In symbols,

Midpt:  ((x1 + x2)/2, (y1 + y2)/2)

I am sure there are good explanations of these concepts in your book, along with diagrams to help you understand.

Answer 2

Question 1:

Imagine a right triangle with:

one side horizontal with an endpoint at one of the given points

another side vertical with an endpoint at the other given point

the hypotenuse the line segment between the two given points.

Now you can easily measure the lengths of the sides of the right triangle.

(X2 - X1) is the length of the horizontal side.

(Y2 - Y1) is the length of the vertical side.

Use the pythagorean theorem...

A^2 + B^2 = C^2

so

(X2 - X1)^2 + (Y2 - Y1)^2 = Distance^2

Distance = sqrt((X2 - X1)^2 + (Y2 - Y1)^2)

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Question 2:

The midpoint will be halfway between these two points, so it will have an X value halfway between the points, and a Y value halfway between the points, or...

( (X2 + X1)/2, (Y2 + Y1)/2 )

Answer 3

1. d=square root of : (X2-X1)^2 + (Y2-Y1)^2. Read as d equals the square root of in parenthese x sub 2 minus x sub 1 parenthese squared plus parentheses y sub 2 minus y sub 1 parenthese squared. (everthing is under the square root except the d= part.

2. (X sub 1 plus X sub 2 all divided by two, Y sub 1 plus Y sub 2 all divided by two)    (X,Y)

Answer 4

Let: D = the distance between two points on a coordinate plane

M = the midpoint between two points on a coordinate plane = (xM, yM)

(x1, y1) = the coordinates of point1

(x2, y2) = the coordinates of point2

D = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

xM = (x2 + x1)/2

yM = (y2 + y1)/2

Example:

Point A: (3, 5)

Point B: (-1, 2)

D = sqrt[(-1 - 3)^2 + (2 - 5)^2]

D = sqrt[(-4)^2 + (-3)^2]

D = sqrt(16 + 9)

D = sqrt(25)

D = 5

xM = (-1+ 3)/2 = 2/2 = 1

yM = (2 + 5)/2 = 7/2 = 3.5

Therefore, the distance between points (3, 5) and (-1, 2) is 5 units.

The midpoint between points (3, 5) and (-1, 2) is at (1, 3.5).

Answer 5

distance = sqrt ( x2-x1)^2 + (y2 - y1)^2)

midpoint = (x2 + x1) / 2   ,  ( y2 + y1) / 2

when i say x1  =  the x coordinate of point 1

when i say x2  =  the x coordinate of point 2

when i say y1  =  the y coordinate of point 1

when i say y2  =  the y coordinate of point 2