Math Homework Help Pleaase..(Geometry)?

Question

Question 1: Three vertices of a triangle are X(2,2) , Y(5,6) and Z(7,2). Is the triangle equilateral, scalene, or iscosceles? explain

Question 2: The point (9,-4) is the midpoint of a segement. One endpoint of the segement is located at (-8,2). Find the other endpoint

Thankss

Answer 1

Question 1:

You need to use the length of a line segment formula (it's just a rearranged version of the Pythagorean Theorem):

length = √[(difference in x)^2 + (difference in y)^2]

Therefore,

XY = √[(5 - 2)^2 + (6 - 2)^2]

= √[(3)^2 + (4)^2]

= √[9 + 16]

= √25

= 5

XZ = √[(7 - 2)^2 + (2 - 2)^2]

= √[(5)^2 + (0)^2]

= √[25 + 0]

= √25

= 5

YZ = √[(7 - 5)^2 + (2 - 6)^2]

= √[(2)^2 + (-4)^2]

= √[4 + 16]

= √20

Since sides XY and XZ are both 5 units in length (and YZ is not), the triangle is iscosceles.

Question 2:

You need to use the midpoint of a line segment formula (which just takes the average of the coordinates of the endpoints):

Given endpoint (-8, 2), let (x, y) be the coordinates of the other endpoint.

Then the coordinates of the midpoint of this line segment are:

((-8+x)/2, (2+y)/2) which is supposed to equal the given midpoint (9,-4).

Therefore, set the x-coordinates of the midpoint equal:

(-8+x)/2 = 9

-8+x = 18

x = 26

And set the y-coordinates of the midpoint equal:

(2+y)/2 = -4

2+y = -8

y = -10

Therefore, the other endpoint is (26, -10).