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3 years ago

Equation of a line that passes through (2,-3) with the slope of 1/2

Mathematics

2 answers:

Irina18 [472]3 years ago

7 0

In point slope form:
y+3=1/2(x-2)

In slope intercept
y= 1/2x-4

Mashcka [7]3 years ago

7 0

The equation fo a line that passe sthrout the point (x1,y1) and having a slope of m is
y-y1=m(x-x1)
given

point i (2,-3) and slope is 1/2
y-(-3)=1/2(x-2)
y+3=1/2(x-2)
y+3=1/2x-1
y=1/2x+2

y=1/2x+2 or y+3=1/2(x-2) or x-2y=-2

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4 years ago

A square has a diagonal length of 10 ft. Draw a diagram and determine the perimeter of the square.

denpristay [2]

The perimeter of the square is: $20\sqrt2$ ft

Step-by-step explanation:

The picture is attached with the answer.

the diagonal of a square divides it into two right angled-triangles.

We can use one of the triangle to find the length of side as the diagonal will be the hypotenuse of the triangle

Let a be the side of the square, then according to Pythagoras theorem

$d^2=a^2+a^2\\(10)^2 = 2a^2\\2a^2=100$

Dividing both sides by 2

$\frac{2a^2}{2}=\frac{100}{2}\\a^2=50$

Taking Square root on both sides

$\sqrt{a^2}=\sqrt{50}\\a=\sqrt{25*2}\\a=\sqrt{5^2 * 2}\\a=5\sqrt{2}\ ft$

Now,

$P = 4a\\P = 4 * 5\sqrt{2}\\=20\sqrt{2}\ ft$

Hence,

The perimeter of the square is: $20\sqrt2$ ft

Keywords: Perimeter, Pythagoras Theorem

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