All categories

3 years ago

The lines below are perpendicular if the slope of the green line is 3/2 what is the slope of the red line

Mathematics

2 answers:

shepuryov [24]3 years ago

8 0

Answer:

The perpendicular line has a slope of -2/3

Step-by-step explanation:

Perpendicular lines have a slope that multiplies to -1

3/2 * m = -1

Multiply each side by 2/3

3/2 * 2/3 *m = -1 * 2/3

m = -2/3

Whitepunk [10]3 years ago

6 0

Answer: -2/3

Step-by-step explanation: The key to understanding this problem is to understand what it means when slopes are perpendicular.

To most students, perpendicular lines are simply

lines that meet at a 90 degree angle.

However, when dealing with these kinds of problems, it's important

to think about perpendicular lines in terms of their slopes.

As a rule, the slopes of two perpendicular

lines are always negative reciprocals.

So if we know that the slope of one line is 3/2, we can find the slope of the other line by finding the negative reciprocal of 3/2.

So we take the fraction and flip it, then we change the sign.

So the negative reciprocal of 3/2 is -2/3.

You might be interested in

Pls pls pls help!!!

cluponka [151]

Answer:

Step-by-step explanation:

there are more money during the week 1 because having a -$8 balance is better than having a -$10 balance, -8 > -10

week 2 has a greater absolute value

| -10| = 10 and |-8| =8 and becasue 10> 8 then |-10| > |-8|

4 0

3 years ago

The triangle and the rectangle below have the same area.

Setler [38]

Answer:

<h2>look at the photo...........................</h2>

7 0

3 years ago

You buy the following materials for the new extension. Calculate the cost of the bricks and cement and then work out the total c

bogdanovich [222]

<u>Answer:</u>

Cost of sand = £150

Cost of bricks = £157.5

Cost of cement = £134

Total cost = £441.50

<u>Step-by-step explanation:</u>

We are given that:

2 tonnes of sand is for £75.00 per tonne,

20 bags of cement are for £6.70 per bag,

350 bricks at 45p each,

So, 2 tonnes of sand at £75.00 per tonne = 2 * £75.00 = £150.00

20 bags of cement at £6.70 per bag = 20 * £6.70 = £134.00

350 bricks at 45p each = 350 * £0.45 = £157.50

Therefore, the total cost of all the materials = £150 + £134 + £157.5 = £441.50

7 0

3 years ago

The points A(1, 4), B(5,1) lie on a circle. The line segment AB is a chord. Find the equation of a diameter of the circle.

tangare [24]

Check the picture below.

well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.

bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.

$\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}$

so, it passes through the midpoint of AB,

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{5+1}{2}~~,~~\cfrac{1+4}{2} \right)\implies \left(3~~,~~\cfrac{5}{2} \right)$

so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{\frac{5}{2}}) \stackrel{slope}{m}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\cfrac{5}{2}}=\stackrel{m}{\cfrac{4}{3}}(x-\stackrel{x_1}{3})\implies y-\cfrac{5}{2}=\cfrac{4}{3}x-4 \\\\\\ y=\cfrac{4}{3}x-4+\cfrac{5}{2}\implies y=\cfrac{4}{3}x-\cfrac{3}{2}$