Q34. 聽Find two values of k such that... [FREE SOLUTION]

魅影直播

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 魅影直播 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 13: Q34. (page 534)

Find two values of k such that the points (-3, 4), (0, k), and (k, 10) are collinear.

Short Answer

Expert verified

The two values of k are $鈭� 5, 6$ .

Step by step solution

Step-1 – Given

The given points are $(鈭� 3, 4), (0, k) and (k, 10)$ .

Step-2 – To determine

We have tofind two values ofk such that the points $(鈭� 3, 4), (0, k) and (k, 10)$ are collinear.

Step-3 – Calculation

The slope formula for two points $(x_{1}, y_{1}) 鈥夆赌塧苍诲鈥夆赌� (x_{2}, y_{2})$ is: $m = \frac{y_{2} 鈭� y_{1}}{x_{2} 鈭� x_{1}}$ .

The given points are $A (鈭� 3, 4), B (0, k) and C (k, 10)$ .

Since the given points are collinear so:

$\begin{array}{l} m_{A B} = m_{B C} = m_{A C} \\ \frac{k 鈭� 4}{0 鈭� (鈭� 3)} = \frac{10 鈭� k}{k 鈭� 0} = \frac{10 鈭� 4}{k 鈭� (鈭� 3)} \end{array}$

Solving this equation, we get:

$\begin{array}{l} m_{A B} = m_{B C} \\ \frac{k 鈭� 4}{0 鈭� (鈭� 3)} = \frac{10 鈭� k}{k 鈭� 0} \\ \frac{k 鈭� 4}{3} = \frac{10 鈭� k}{k} \\ k (k 鈭� 4) = 3 (10 鈭� k) \\ k^{2} 鈭� 4 k = 30 鈭� 3 k \\ k^{2} 鈭� k 鈭� 30 = 0 \\ k^{2} 鈭� 6 k + 5 k 鈭� 30 = 0 \\ k (k 鈭� 6) + 5 (k 鈭� 6) = 0 \\ (k 鈭� 6) (k + 5) = 0 \\ k 鈭� 6 = 0 \\ k = 6 \\ k + 5 = 0 \\ k = 鈭� 5 \end{array}$

So, the two values of k are $鈭� 5, 6$ .

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魅影直播

Find two values of k such that the points (-3, 4), (0, k), and (k, 10) are collinear.

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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