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1 year ago

Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?

Mathematics

2 answers:

Marta_Voda [28]1 year ago

8 0

Answer: The required equation of line BC is $x=4.$

Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).

We are to find the equation of line BC.

We know that the slope of a line passing through the points (a, b) and (c, d) is given by

$m=\dfrac{d-b}{c-a}.$

So, the slope of the line AB will be

$m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.$

Therefore, the equation of the line AB is

$y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.$

Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.

So, its equation will be of the form

x = constant.

Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have

$x=4.$

Thus, the required equation of line BC is $x=4.$

andrey2020 [161]1 year ago

4 0

The correct answer is:

x=4.

Explanation:

The slope of line AB is given by the formula
 $m=\frac{y_2-y_1}{x_2-x_1}$ 

Using the coordinates of A and B, we have
 $m=\frac{4-4}{4--3}=\frac{0}{7}=0$ 

Perpendicular lines have slopes that are negative reciprocals. Since the slope of AB is 0/7, the reciprocal is 7/0, which is undefined.

Any line with an undefined slope is a vertical line. This will be a vertical line that passes through point B.

Vertical lines have the equation x=c, where c is a constant; since it runs through B, which has coordinates (4, 4), this means the equation is x=4.

You might be interested in

The probability that an Oxnard University student is carrying a backpack is .70. If 10 students are observed at random, what is

Rus_ich [418]

Answer:

35.03% probability that fewer than 7 will be carrying backpacks

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they are carrying a backpack, or they are not. The probability of a student carrying a backpack is independent from other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability that an Oxnard University student is carrying a backpack is .70.

This means that $p = 0.7$

If 10 students are observed at random, what is the probability that fewer than 7 will be carrying backpacks

This is $P(X < 7)$ when $n = 10$ . So

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.7)^{0}.(0.3)^{10} = 0.000006$

$P(X = 1) = C_{10,1}.(0.7)^{1}.(0.3)^{9} = 0.0001$

$P(X = 2) = C_{10,2}.(0.7)^{2}.(0.3)^{8} = 0.0014$

$P(X = 3) = C_{10,3}.(0.7)^{3}.(0.3)^{7} = 0.0090$

$P(X = 4) = C_{10,4}.(0.7)^{4}.(0.3)^{6} = 0.0368$

$P(X = 5) = C_{10,5}.(0.7)^{5}.(0.3)^{5} = 0.1029$

$P(X = 6) = C_{10,6}.(0.7)^{6}.(0.3)^{4} = 0.2001$

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.000006 + 0.0001 + 0.0014 + 0.0090 + 0.0368 + 0.1029 + 0.2001 = 0.3503$

35.03% probability that fewer than 7 will be carrying backpacks

4 0

2 years ago

marcus can buy 0.3 pound of sliced meat from a deli for $3.15 how much will 0.7 pound of sliced meat cost?

ddd [48]

$22.05 because $3.15 times 0.7 is= 22.05

7 0

1 year ago

Read 2 more answers

-6/5 divided by 12/25

Tema [17]

Answer:

-1 17/25

Solution with Steps

−65−1225=?

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(-6/5, 12/25) = 25

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(−65×55)−(1225×11)=?

Complete the multiplication and the equation becomes

−3025−1225=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

−30−1225=−4225

This fraction cannot be reduced.

The fraction

−4225

is the same as

−42÷25

Convert to a mixed number using

long division for -42 ÷ 25 = -1R17, so

−4225=−11725

Therefore:

−65−1225=−11725

4 0

2 years ago

Angela is getting a pedicure at a spa that also offers massages where customers pay by the minute. If Angela only gets a pedicur

saveliy_v [14]

This is an expression if she only gets pedicure
y = 35

If she wants to get massage, multiply the cost for a minute with the number of minutes.
Find cost per minute first
cost = 50/20
cost = 2.5

So the expression would be
y = 35 + 2.5x
y = 2.5x + 35

5 0

2 years ago

GaryK [48]

Answer:

the answer is $5,000

Step-by-step explanation:

the question is asking what the initial value of the painting is and in the equation, they are trying to find out how much the painting will cost after t years. the 1.098 is how much the painting decreases each year and it is being multiplied by &5000 so $5000 is the original value of the painting.

5 0

1 year ago