1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
saw5 [17]
3 years ago
13

. Given ????(5, −4) and T(−8,12):

Mathematics
1 answer:
damaskus [11]3 years ago
7 0

Answer:

a)y=\dfrac{13x}{16}-\dfrac{129}{16}

b)y = \dfrac{13x}{16}+ \dfrac{37}{2}

Step-by-step explanation:

Given two points: S(5,-4) and T(-8,12)

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: y = mx + c where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

m = \dfrac{y_2 - y_1}{x_2 - x_1}

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

m = \dfrac{12 - (-4)}{(-8) - 5}

m = \dfrac{-16}{13}

to find the perpendicular of this gradient: we'll use:

m_1m_2=-1

both m_1and m_2 denote slopes that are perpendicular to each other. So if m_1 = \dfrac{12 - (-4)}{(-8) - 5}, then we can solve for m_2 for the slop of ther perpendicular!

\left(\dfrac{-16}{13}\right)m_2=-1

m_2=\dfrac{13}{16}:: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope m and the points (x,y). And plug into the equation: (y - y_1) = m(x-x_1)

side note: you can also use the y = mx + c to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

(y - y_1) = m(x-x_1)

we have the slope of the perpendicular to ST i.e m=\dfrac{13}{16}

and the line should pass throught S as well, i.e (5,-4). Plugging all these values in the equation we'll get.

(y - (-4)) = \dfrac{13}{16}(x-5)

y +4 = \dfrac{13x}{16}-\dfrac{65}{16}

y = \dfrac{13x}{16}-\dfrac{65}{16}-4

y=\dfrac{13x}{16}-\dfrac{129}{16}

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for T(-8,12)

(y - y_1) = m(x-x_1)

(y -12) = \dfrac{13}{16}(x+8)

y = \dfrac{13x}{16}+ \dfrac{104}{16}+12

y = \dfrac{13x}{16}+ \dfrac{37}{2}

this is the equation of the line that is perpendicular to ST and passes through T

You might be interested in
1. Tamara draws a tile from a bag and records the results. The bag contains tiles labeled, WATER, M, EL. O, and N. Based on this
Katen [24]

Answer:

u think b

Step-by-step explanation:

becuse she is mor likely to draw a vowel

6 0
3 years ago
Read 2 more answers
The seventh-grade class is building target areas for a PE activity. The bases for the game will be circular in shape. The diamet
Scilla [17]
To calculate the area it is pi*r^2

so since r = 1/2 d

2.5^2 * pi = area
or
19.625
8 0
3 years ago
Two cars leave the same parking lot, with one heading north and the other heading east.
Otrada [13]

Answer:

wouldn't it be 3 kilometers because 3 this way plus 3 that way = 6 away from each other?

8 0
3 years ago
I need help with question 30..
Aloiza [94]

Let's say 1000 dollars was spent on all of these. That would mean 170 dollars and 240 were spent on food and entertainment respectivly. If we want to see how much of the total cost was spent on these things, we would have to add them and divide them by 1000, so:

\frac{170+240}{1000}=\frac{410}{1000}=frac{41}{100}

6 0
3 years ago
What is the volume of the sphere, rounded to the nearest cubic foot?
Zielflug [23.3K]

Given:

Radius = 5 ft

To find:

The volume of the sphere

Solution:

Volume of the sphere:

$V=\frac{4}{3}\pi r^3

$V=\frac{4}{3}\times 3.142 \times 5^3

$V=523.66

$V=524

The volume of the sphere is 524 ft³.

3 0
3 years ago
Other questions:
  • (x-6)(x+2) hi am am stuck can someone answer asap
    5·1 answer
  • HELP QUICKIE!!!
    15·1 answer
  • AC is tangent to circle o at point c. what is the length of ac?​
    15·1 answer
  • Based on the family the graph below belongs to, which equation could represent the graph? image below.
    9·1 answer
  • Write 7.3 x 10 to the -7th power in standard form.
    15·2 answers
  • Find an expression for the nth term (tn) in each of the following sequence:
    12·1 answer
  • 3)An inch is equal to about 2.54 centimeters. Write an expression that estimates the number of centimeters in "x" inches. Then,
    9·1 answer
  • A. 20 mph<br> B. 35 mph<br> C. 70 mph<br> D. 100 mph
    15·2 answers
  • Angela is getting a pedicure at a spa that also offers massages where customers pay by the minute. If Angela only gets a pedicur
    7·1 answer
  • Please Explain How to Solve.
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!