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3 years ago

What are the coordinates of the point (-4,-10) after a 180 rotation about the orgin and then a translation 1 unit right

Mathematics

1 answer:

goblinko [34]3 years ago

5 0

1. Rotation by 180° (clockwise or anti-clockwise) about the origin has a rule:

(x,y)→(-x,-y).

Then

(-4,-10)→(4,10).

2. Translation 1 unit to the right has a rule:

(x,y)→(x+1,y).

Then

(4,10)→(5,10).

3. After rotation and translation the image of point (-4,-10) is point (5,10).

Answer: (5,10).

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2 years ago

A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The

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Using the Sine rule,

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Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

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$A^0+P^0+B^0=180^0$ $\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}$

Using the side rule to find the length of wire BP,

$\begin{gathered} \frac{\sin 60^0}{y}=\frac{\sin 80^0}{14} \\ \text{Crossmultiply,} \\ y\times\sin 80^0=14\times\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=\frac{14\times\sin 60^0}{\sin 80^0} \\ y=12.31m \end{gathered}$

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).

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1 year ago

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(a+b)=sqrt(d)

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What value of x makes the equation 6x + 12 = 42 true?

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-12. -12

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