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3 years ago

15

How do you determine if the line segments are congruent

2 answers:

Jet001 [13]3 years ago

6 0

You can know if they are congruent by the length of both lines! <span />

Gemiola [76]3 years ago

4 0

You must calculate the length of the segments.

Suppose segments AB and CD
Being A (m, n), B (p, q) C(r,s) and D(t,u)
<span>
They are congruent if:

</span> $\boxed{(p-m)^2+(q-n)^2=(t-r)^2+(u-s)^2}$ <span>

</span>

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Find the equation in standard form of the line passing through the points 3,-4 and 5,1

aliina [53]

Answer:

5x - 2y - 23 = 0

Step-by-step explanation:

Line is passing through the points $(3,\:-4)= (x_1, \:y_1) \: \&\: (5,\: 1)= (x_2,\:y_2)$

Equation of line in two point form is given as:

$\frac{y -y_1 }{y_1 -y_2 } = \frac{x -x_1 }{x_1 -x_2 } \\ \\ \therefore \: \frac{y -( - 4) }{ - 4 -1} = \frac{x -3 }{3 -5 } \\ \\ \therefore \:\frac{y + 4 }{ - 5} = \frac{x -3 }{ - 2 } \\ \\ \therefore \: \frac{y + 4 }{ 5} = \frac{x -3 }{ 2 } \\ \\ \therefore \: 2(y + 4) = 5(x - 3) \\ \therefore \: 2y + 8 = 5x - 15 \\ \therefore \: 5x - 15 - 2y - 8 = 0 \\ \red{ \boxed{ \bold{\therefore \: 5x - 2y - 23 = 0}}} \\ is \: the \: required \: equation \: of \: line \: in \: \\ standard \: form.$

7 0

3 years ago

for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).

Schach [20]

Answer:

k = 18

=========

<h2>Given</h2>

<h3>Line 1</h3>

3x - ky + 7 = 0

<h3>Line 2</h3>

Passing through the points (4, 3) and (5, - 3)

<h2>To find</h2>

The value of k, if the lines are perpendicular

<h2>Solution</h2>

We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.

Find the slope of line 1 by converting the equation into slope-intercept from standard form:

<u><em>Info:</em></u>

<em>standard form is ⇒ ax + by + c = 0, </em>
<em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>

3x - ky + 7 = 0
ky = 3x + 7
y = (3/k)x + 7/k

Its slope is 3/k.

Find the slope of line 2, using the slope formula:

m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6

We have both the slopes now. Find their product:

(3/k)*(- 6) = - 1
- 18/k = - 1
k = 18

So when k is 18, the lines are perpendicular.

4 0

1 year ago

Emerson struck out 112 times in 350 at-bats. What is the percent of strike outs per at-bat?

Natasha2012 [34]

We are told that Emerson struck out 112 times in 350 at-bats. We are asked to find the percent of strike outs per at-bat.

Let us find out 112 is what percent of 350.

$\text{Percentage of strike outs per at-bat}=\frac{112}{350} \cdot 100$

$\text{Percentage of strike outs per at-bat}=0.32 \cdot 100$

$\text{Percentage of strike outs per at-bat}=32$

Therefore, Emerson struck out 32% of the at-bats.

6 0

3 years ago

Choose the product. a 3 b 2 · 4ab 3 <br><br> 4a3b5<br><br> 4a3b6<br><br> 4a4b5

zvonat [6]

A³ b² 4ab³

Rearrange order:

4 a³ a b² b³

Now add up the exponents from same base:

4 a³⁺¹ b²⁺³

4 a⁴ b⁵

Final answer: 4 a⁴ b⁵

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3 years ago

Solve each system of equations

marishachu [46]

Answer:

1. x = 7/2 + 5y/2

2. x = 3/4 - 5y/8

3. x = 1/8 = 5y/8

Step-by-step explanation:

Thats all i can do. Its too confusing

3 0

3 years ago

Read 2 more answers