Question

Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all of your work to receive credit.

Answer 1

plz help!!!

Answer 2

@ganeshie8

Answer 3

find the slope of BC
find the slope of EF

Answer 4

show that they're opposite and reciprocals of each other

Answer 5

wait let me find the slope

Answer 6

start by finding the coordinates of B and C :

B = ?
C = ?

Answer 7

for b i got 1 @ganeshie8

Answer 8

and for c i got -1

Answer 9

what do i do next

Answer 10

conclude

Answer 11

??

Answer 12

slope of AB = 1
slope of EF = -1

so, slope of EF = -1 = -(1/1) = -1/(slope of AB)

hence the slope of AB and EF are opposite and reciprocals of each other

Answer 13

thats it thats all i write??

Answer 14

yes and may be add one more line :
Since AB and EF are perpendicular lines, it proves that perpendicular lines have opposite and reciprocal slopes.

Answer 15

can u help me with another one?

Determine if triangle XYZ with coordinates X (1, 1), Y (5, 6), and Z (6, 2) is a right triangle. Use evidence to support your claim. If it is not a right triangle, what changes can be made to make it a right triangle? Be specific.

Answer 16

can u help me??

Answer 17

use distance formula and find all the 3 side lengths

Answer 18

what do i do after

Answer 19

length of side XY = ?
length of side YZ = ?
length of side ZX = ?

Answer 20

next use the converse of pythagorean theorem :

if `a^2 = b^2 + c^2`, then the triangle is right triangle

Answer 21

@ganeshie8

Answer 22

@ganeshie8

Answer 23

i did the distance formula

Answer 24

for xy i got 6.4

Answer 25

for yz i got 4.1

Answer 26

for zx i got 5.1

Answer 27

may be keep them in radicals

Answer 28

so if i keep them i n radicals i get

Answer 29

41, 17, and 26

Answer 30

XY = \( \sqrt{41}\)
YZ = \( \sqrt{17}\)
ZX = \( \sqrt{26}\)

Answer 31

yes what do i do

Answer 32

now?

Answer 33

squaring them gives you


XY^2 = 41
YZ^2 = 17
ZX^2 = 26

Answer 34

Notice that XY^2 = YZ^2 + ZX^2

Answer 35

So, by converse of pythagorean theorem, the given triangle is a right triangle.

Answer 36

do i have to plug thenm in and solve?

Answer 37

nothing to solve here,
just show that the square of one side equals the sum of squares of other two sides

Answer 38

YZ^2 + ZX^2 = 17 + 26
= 41
= XY^2

Answer 39

so what should i write as my answer?

Answer 40

everything we discussed so far

Answer 41

show the distance formula, and show your work on how you found the lengths of sides using it

Answer 42

then show that the sum of squares of two sides equals the square of other side