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3 years ago

Find the distance between the points given. (3, 4) and (4, 7) √(10) 3 2√2

Mathematics

1 answer:

Tom [10]3 years ago

5 0

Answer:

Step-by-step explanation:

givens

x1 = 3

x2 = 4

y1 = 4

y2 = 7

formula

d = sqrt( (x1 - x2)^2 + (y1 - y2)^2 )

solution

d = sqrt( (3 - 4)^2 + (4 - 7)^2 )

d = sqrt ( 1 + 3^2)

d = sqrt( 1 + 9)

d = sqrt( 10)

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What are the coordinates of point B on \overline{AC} such that AB = 1/2 BC

marta [7]

Answer:

C. $B(x,y) = \left(3,-\frac{16}{3} \right)$

Step-by-step explanation:

Let $A(x,y) = (6,-7)$ , $B(x,y) = (x,y)$ and $C(x,y) = (-3,-2)$ . From statement we know that $AB = \frac{1}{2}\cdot BC$ , which is equivalent to the following linear algebraic formula:

$B(x,y) -A(x,y) = \frac{1}{2}\cdot [C(x,y)-B(x,y)]$ (1)

$B(x,y)-A(x,y) = \frac{1}{2}\cdot C(x,y)-\frac{1}{2}\cdot B(x,y)$

$\frac{3}{2}\cdot B(x,y) = \frac{1}{2}\cdot C(x,y)+A(x,y)$

$B(x,y) = \frac{1}{3}\cdot C(x,y) +\frac{2}{3}\cdot A(x,y)$ (2)

Then, the coordinates of point B on AC are:

$B(x,y) = \frac{1}{3}\cdot (-3,-2)+\frac{2}{3}\cdot (6,-7)$

$B(x,y) = \left(-1, -\frac{2}{3}\right)+\left(4, -\frac{14}{3} \right)$

$B(x,y) = \left(3,-\frac{16}{3} \right)$

Which means that correct answer is C.

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salantis [7]

Answer:

Step-by-step explanation:

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Write the equation for 5x + 2y = 3 in slope-intercept form. 11

Nastasia [14]

5x+2y=3
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rewrite in order (optional depending on teacher)
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