Question

Could somebody help me understand this SAT Prep question

Answer 1

the explanation is below, what is not clear there

Answer 2

I don't get it.

Answer 3

Is not clear enough

Answer 4

ok, just start doing the things the paragraph says, plot R and plot S maybe if you want first

Answer 5

can't tell where point T is yet,

they also tell you that the sum of the 3 slopes for the sides of the triangle add up to 1,
first get the slope of the thing ya know RS, 3/3 or 1

just that side has the entire slope sum..how can that be, if you have to add 2 more sides to that?

Answer 6

recall using the same idea for calculating the slope, a horizontal line has a slope = 0, and a vertical line has a undefined slope (rise/0)-und.

Answer 7

so for the two remaining sides to not have slope values, since RS already is the entire total slope of 1,

the two unknown sides must be horizontal and vertical, and perpendicular to each other

Answer 8

So since the slope is = 1 is 45°

Answer 9

I get horizontal so its sum is equal to zero but why vertical ?

Answer 10

And perpendicular to each other ?

Answer 11

that is true a line slope 1 forms a 45 angle with the x axis, or the horizontal side, but not really needed to solve the prob

Answer 12

vertical has an undefined slope, rise/run is some rise an d zero run, that is undefinedm dividing by 0

Answer 13

horizontal slope - 0 / # = 0
vertical slope - # / 0 = undefined

Answer 14

I get that but I don't understand why you say the other two have to be horizontal, vertical and perpendicar go each other ? Is because it is a triangle ?

Answer 15

*to each other

Answer 16

the sum of the 3 slopes for the sides of this triangle total to 1
the given side has slope 1, the remaining 2 sides must not have any slope value

Answer 17

oh the answer is A - NONE of the angles are right, forget that,

i thought adding a undefined slope would break something, forget all that..

Answer 18

And because they need to intersect it is impossible

Answer 19

so the remaining two sides should have 2 slopes that total to 0, right, one + and one -

Answer 20

And is it possible to get such triangle ?

Answer 21

random point T(x,y)q

Answer 22

I get that but I don't get how to get the other two line segments

Answer 23

Total of 3 sides slopes = 1
slope RS = 1
so
slope of RT and slope of RS will have the same value, but opposite sign

Answer 24

sorry RT and TS must have same slopes with opposite sines +/-, since they have to total to 0

Answer 25

Ohh OK. I see however how would that look like ?

Answer 26

Would that actually form a triangle ?

Answer 27

yes, you can make a triangle with those conditions, but not a right triangle i am pretty sure,

slope RT = (y - 3)/(x - 2)
Slope ST = (y - 6) / (x - 5)

Answer 28

could you please please draw it? is just hard to visualize it :(

Answer 29

i mean the possible triangle based on those slopes

Answer 30

those must total to 0 , so

slope RS = - slope ST
or
- slope RS = slope ST


the possible point can be above RS or below, forming a parallelogram

Answer 31

start at R , go to T with a neg slope, then from T to S with the same positive slope, there are probably infinite answers, you can get the coordinate of T(x,y) as a equation y in terms of x, and that will have the possible solution values i think,

in either case, there will be no 90 angles in the triangle,

Answer 32

none of those slopes can be perpendicular

Answer 33

in general
slopes 1 , +m, and -m total to 1 like it says

+m and -m are not perpendicular, recall perpendicular slopes are m and -1/m

Answer 34

to be perpenticular it was need an undefined slope and a horizontal one

Answer 35

needed*

Answer 36

to be perpendicular to RS with slope 1 , you need a slope of -1/1 = -1

then the third slope would also have to be +1 to total all 3 to 1,

that will not make a triangle, you have 2 sides that are parallel with sloipe 1

Answer 37

that shows you cant have a right angle triangle with those givens

slopes in the triangle sides are --- 1 , +m , -m

cant do it and have a right angle

Answer 38

you can do what i think i was trying, solve th eslopes as a equation of y and x

y(x) may say what points actually will work, the possible intervals

Answer 39

I thought to have a right traingle you needed a horizontal line. A slope of 1 and an undefined slope

Answer 40

yeah i said that at first also as a way to make a right triangle here, but adding undefined slope doesnt give 1 for the total of the 3 slopes, no vertical line possible

Answer 41

sooo to see that i am understanding

Answer 42

1 + 0 + undefined = undefined, not 1

Answer 43

The part that i am confused on is that you say that you can make a right triangle by having slopes 1, -m and m

I know that is the only way to have a slope of 1 but those that actually makes a right triangle?

Answer 44

does that *

Answer 45

no i am saying that it is impossible to make a right triangle, just from that fact.

+m and -m, not right angle

a right angle to RS will create a side with slope -1/1 or -1
this is not possible with the rules

Answer 46

-1/1 what do you mean?

Answer 47

in the case you draw a perpendicular line to RS, and try that way, no way to make a triangle , the slopes will be

1 , -1 , 1

2 sides are parallel slope 1, not triangle

Answer 48

RS has slope 1, if you want a right angle at R or S, the slope or RT or ST will become -1/1 = -1

a perpendicular slope is the negative reciprical of the given slope

Answer 49

ohh ok I see

Answer 50

ohh i see what you are saying now. It is impossible because based on the given conditions, if you want to slopes to add up to 3 to line segments need to be parallel

Answer 51

two line segments*

Answer 52

just for fun, since RT and ST have opposite slopes, plugging in the values and solving for y in

slope RT = - slopeST

i got

\[y = \frac{ 9x - 27 }{ 2x -7 }\]

those values are the possible (x,y) points that work to make a triangle

Answer 53

How you did that?

Answer 54

just let T be an arbitrary point T(x,y)

the slopes RT and ST can be formed with that, then equate them and make one the negative of the other, solve for y

Answer 55

notice there is a vertical asmytpe value when x=7/2, the denominator in that becomes 0

i bet when x=7/2, that is where you can get the standard horizontal vertical right triangle with RS

Answer 56

no right triangle possible, and from y(x) there, any other value you want for x, and the resulting y, will work for the point T to make a triangleRST

Answer 57

lol, i am done, for the actual prob

realize side slopes 1, +m,-m
can not make a right angle at any of those vertex points

Answer 58

Thanks i got do confused after that lol

Answer 59

Thanks a lot for taking The time to explain to me :)

Answer 60

no prob, you can make any triangle you wish, any point i think will work, except (7/2 , 0) and the mirror point over RS

the location for T can be anything but that, and have slope values arbitrarily close to vertical or horizontal,