Mathematics College

A line passes through R(6, 9) and K(-6, 15)
a) What is the slope of RK?
b) Line VB is parallel to RK. What is the slope of VB?
c)Line WX is perpendicular to RK. What is the slope of WX? ​

Answers

Answer 1

The slope of line WX is 2.Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which means we flip the fraction and change its sign:

slope of WX = -1 / (-1/2) = 2.

a) To find the slope of the line RK, we can use the formula:

slope = (change in y) / (change in x)

Given the points R(6, 9) and K(-6, 15), we can calculate the change in y and change in x:

change in y = 15 - 9 = 6

change in x = -6 - 6 = -12

Plugging these values into the slope formula:

slope = (6) / (-12) = -1/2

Therefore, the slope of line RK is -1/2.

b) Since line VB is parallel to line RK, it will have the same slope as RK. Therefore, the slope of line VB is also -1/2.

c) To find the slope of line WX, which is perpendicular to RK, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. Since the slope of RK is -1/2, the slope of WX will be the negative reciprocal of -1/2, which is 2.

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Related Questions

[2.4-(0.3-3.21)·2+0.44÷(-2)]÷2/5 pls help me asap I litteraly have no idea how to do this

Answers

the final answer is 0.149

0.3-3.21= -2.91
-2.91 * 2= -5.82
2.4 - 5.82= -3.42
-3.42 + 0.44= -2.98
-2.98 / -2= 1.49
1.49 / 2= 0.745
0.745 / 5= 0.149

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Answers

The converse of the parallelogram angle theorem is proved.

How to explain the information

The term parallelogram is defined as a quadrilateral whose two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle and then the quadrilateral.

Here we are given that  LM ≅ ON and  LO ≅ MN

Here we have also know that ∠LNO and ∠NLM are alternative and interior angles

Then according to the reflexive property, it can be written as

=> LN ≅ LN

Then as per the SSS similarity the given triangle is written as,

ΔLNO ≅ ΔNLM

Here we have also it can be written as ∠OLN ≅ ∠MNL and  ∠LNO ≅ ∠NLM

Then it can be written as LM || ON and  LO || MN

Then the LMNO is a parallelogram

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The measure of the largest scale of a triangle is 40o more than the measure of the smallest angle, and the measure of the remaining angle is 20o more than the measure of the smallest angle. Find the measure of each angle.

Answers

Answer:

  40°, 60°, 80°

Step-by-step explanation:

You want the measures of the three angles of a triangle if the larger angles are 20° and 40° greater than the smallest.

Middle angle

The largest angle is 20° more than the middle angle, and the smallest is 20° less. Then the sum of the three angles is 3 times the middle angle, which must be 180°/3 = 60°.

The three angles are 40°, 60°, 80°.

__

Additional comment

If you need equations, you can designate the angles a, b, c, smallest to largest. Then c=a+40, and b=a+20. The sum is ...

  (a) +(a +20) +(a +40) = 3a +60 = 180

Dividing by 3 tells you ...

  a +20 = 60 . . . . . matches the value of b

  a = 60 -20 = 40

  c = 40 +40 = 80

If we were to write the equations in terms of b, we would have ...

  (b -20) +b +(b +20) = 180

  3b = 180

  b = 60

This version gives a 1-step equation to solve instead of a 2-step equation, easier to do mentally.

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The measure of the Angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.

The measure of the smallest angle as x.

According to the given information, the largest angle is 40 degrees more than the smallest angle. Therefore, the measure of the largest angle is x + 40.

Similarly, the remaining angle is 20 degrees more than the smallest angle. So, the measure of the remaining angle is x + 20.

The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:

x + (x + 40) + (x + 20) = 180.

Simplifying the equation, we have:

3x + 60 = 180.

Subtracting 60 from both sides of the equation:

3x = 120.

Dividing both sides by 3:

x = 40.

Therefore, the measure of the smallest angle is 40 degrees.

Using this value, we can find the measures of the other two angles:

The largest angle is x + 40 = 40 + 40 = 80 degrees.

The remaining angle is x + 20 = 40 + 20 = 60 degrees.

the measure of the angles in the triangle are: the smallest angle is 40 degrees, the largest angle is 80 degrees, and the remaining angle is 60 degrees.

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