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Stolb23 [73]
3 years ago
6

What is the distance, in units, between the points

, -6)" alt="(2, -6)" align="absmiddle" class="latex-formula">and (-4, 3)? Express your answer in simplest radical form.
Mathematics
1 answer:
Anna71 [15]3 years ago
6 0

Answer: 3\sqrt{13}

Step-by-step explanation:

\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

\sqrt{\left(-4-2\right)^2+\left(3-\left(-6\right)\right)^2}

=3\sqrt{13}

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Step-by-step explanation:

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The coordinates of the endpoint of QS are Q(-9,8) and S(9,-4). Point R is on cue as such that QR:RS Is in the ratio 1:2. What ar
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R(–3, 4)

Step-by-step explanation:

Let Q(-9,8) and S(9,-4) be the given points and let R(x, y) divides QS in the ratio 1:2.

By section formula,

R(x, y)=R\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)

Here, x_{1}=-9, y_{1}=8, \text { and } x_{2}=9, y_{2}=-4 \text { and } m=1, n=2

Substituting this in the section formula

R(x, y)=R\left(\frac{1(9)+2(-9)}{1+2}, \frac{1(-4)+2(8)}{1+2}\right)  

To simplifying the expression, we get

\Rightarrow R(x, y)=R\left(\frac{9-18}{3}, \frac{-4+16}{3}\right)

\Rightarrow R(x, y)=R\left(\frac{-9}{3}, \frac{12}{3}\right)

⇒ R(x,y) = R(–3,4)  

Hence, the coordinates of point R is (–3, 4).

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