We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.

The distance of a point to a line is the length of the perpendicular from the line to the point.

So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:

4x + 5y = 4(-1)+5(3) = 11

Those lines meet at the foot of the perpendicular, which is what we're after.

4x + 5y = 11

5 x - 4y = 10

We eliminate y by multiplying the first by four, the second by five and adding.

16x + 20y = 44

25x - 20y = 50

41x = 94

x = 94/41

y = (11 - 4x)/5 = 15/41

We want the distance from (-1,3) to (94/41,15/41)

$d = \sqrt{ (-1 - 94/41)^2 + (3 - 15/41)^2 } = \dfrac{27}{\sqrt{41}}$

8 0

4 years ago

The Golden family is planning to buy a house that sells for $125,000. They want to put 20% as a down payment. How much would the

Vadim26 [7]

Answer:

100000

Step-by-step explanation:

You multiple 125000 with .20 you get 25000 then you subtract 25000 fro 125000 and you get 100000 and that's your answer.

6 0

3 years ago

Find (f+g)(x) f(x)=-3x+2 g(x)=x^3

melomori [17]

f+g (x) = 3x+2 + x^3

= x^3+3x+2

5 0

3 years ago

Quadratic equation x² - 5x+6=0

Nadusha1986 [10]

Answer: X=6-1

Step-By-Step Equation:

6 0

3 years ago