Question

help

Answer 1

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:

A graph titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,63, B at ordered pair 1, 105, A at ordered pair 2, 147, and the ordered pair 3,189.

Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)
Part B: What are the initial value and slope of the graph, and what do they represent? (6 points)

Answer 2

@Michele_Laino

Answer 3

I consider your drawing:

Answer 4

now, if we look at the two little triangles, then we can write this:
\[\frac{{BM}}{{CM}} = \frac{2}{1},\quad \frac{{AN}}{{BN}} = \frac{2}{1}\]
furthermore, angles ANB and BCM are congruent each other, so using the SAS criterion, we can say that both triangles CMB and BNA are....?

Answer 5

ok so can you explain the answer for prt A and B

Answer 6

please note that what I have written before, is an explanation for part A

Answer 7

ok please dont leave i will brb

Answer 8

are the triangles CMB and BNA similar each other?

Answer 9

@Michele_Laino im back can you come back and help me now please

Answer 10

please read what I have written before

Answer 11

you have to count the little squares into your drawing

Answer 12

is that the answer for part A above???

Answer 13

yes!

Answer 14

It is the reasoning that we have to do in order to get the corresponding answer

Answer 15

so whats B

Answer 16

for part B.
the initial value is the \(y-\) coordinate of point \(C\)

Answer 17

so wait the answer for part A is BMCM=21,ANBN=21

Answer 18

the answer to part A. is not a value. Part A asks to you to give a reasoning

Answer 19

angles ANB and BCM are congruent each other, so using the SAS criterion, we can say that both triangles CMB and BNA are.non congruent



so that the answer for part A ^?

Answer 20

triangles CMB an BNA are congruent, by the SAS criterion

Answer 21

so thats part A

Answer 22

?

Answer 23

more precisely I have to consider the subsequent triangles:

namely the orange triangle CMB and the green triangle CNA

Answer 24

we can say that triangles CMB and CNA are similar each other, since if you count the little square of your drawing, you will find this quantities:
\[\Large \frac{{BM}}{{CN}} = \frac{2}{1},\quad \frac{{AN}}{{CN}} = \frac{4}{2}\]
namely the corresponding sides are proportional each other

Answer 25

triangles CMB an BNA are congruent, by the SAS criterion
is that for part A

Answer 26

furthermore angles BMC and ANC are 90 degrees both, so they are congruent

Answer 27

please, we have to consider triangles CMB and CNA

Answer 28

and we can say that triangle CMB and CNA are similar for SAS criterion

Answer 29

triangles*

Answer 30

ok so can you write the answer for part A im confused

Answer 31

so the common ratio:\[\frac{{BM}}{{CN}} = \frac{{AN}}{{CN}} = 2\]
represents the slope of the line

Answer 32

ok so BMCN=ANCN=2
is the answer?

Answer 33

In other words, we can speak about a slope of the line, since the two triangles CMB and CNA are similar each other

Answer 34

a possible answer can be this:
"Since the two triangles CMB and CNA are similar each other, than there is a unique value for the ratios \[\frac{{BM}}{{CN}},\quad \frac{{AN}}{{CN}}\]
and such value is the slope of the line along the points \(C,B,A\)"

Answer 35

ok thats for A and what for B? this

the initial value is the y− coordinate of point C

Answer 36

yes! what is the \(y-\) coordinate of \(C\)?

Answer 37

63?

Answer 38

correct!