Find the distance between points P(5,8) and Q(1,7) to the nearest tenth

Mathematics

1 answer:

morpeh [17]3 years ago

3 0

Answer:

$length = \sqrt{ {(x _{1} - x_{2} )}^{2} + {(y _{1} - y_{2} })^{2} } \\ = \sqrt{ {(5 - 1)}^{2} + {(8 - 7)}^{2} } \\ = \sqrt{16 + 1 } \\ = \sqrt{17} \\ length = 4.1 \: units$

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Given a triangle ABC at A = ( - 1, 3 ) B = ( 1, - 1 ) C = ( 2, 2 ) and if the triangle is rotated 90 ° clockwise about the point

lidiya [134]

Answer:

The coordinates of A' are (6,6).

Step-by-step explanation:

It is given that in triangle ABC, A = (-1, 3), B = (1, - 1) and C = (2, 2).

If a point is rotated 90 ° clockwise about the point ( a,b ), then

$(x,y)\rightarrow ((y-b)+a,-(x-a)+b)$

It is given that the triangle is rotated 90 ° clockwise about the point ( 4, 1 ). So, a=4 and b=1.

$(x,y)\rightarrow ((y-1)+4,-(x-4)+1)$

$(x,y)\rightarrow (y+3,-x+5)$

The coordinates of A are (-1,3), So, the coordinates of A' are

$A(-1,3)\rightarrow A'(3+3,-(-1)+5)$

$A(-1,3)\rightarrow A'(6,6)$

Therefore the coordinates of A' are (6,6).

7 0

3 years ago

13. WILL MARK BRAINLIEST!! HELP!

Umnica [9.8K]

Answer:

$\large\boxed{\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9x}=\dfrac{9x}{x-8}}$

Step-by-step explanation:

$\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9x}=\dfrac{x+2}{x^2+2x-8x-16}\cdot\dfrac{9x}{1}\\\\=\dfrac{(x+2)(9x)}{x(x+2)-8(x+2)}=\dfrac{(x+2)(9x)}{(x+2)(x-8)}\\\\\text{cancel}\ (x+2)\\\\=\dfrac{9x}{x-8}$