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Geometry

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

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 13: Q. 25 (page 533)

A line with slope m passes through points (p, q) and (r, ?).

Short Answer

Expert verified

A line with slope $m$ passes through points $(p, q) and (r, m r - m p + q)$

Step by step solution

01

Step-1 – Given

A line with slope $m$ passes through points $(p, q) and (r, ?)$

02

Step-2 – To determine

We have tofind the unknowny coordinate of the given point.

03

Step-3 – Calculation

The slope formula for two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The given points are $(p, q) and (r, ?)$ .

Let = the unknown x coordinate

So,

$\begin{array}{l} m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\ m = \frac{y_{2} - q}{r - p} \\ y_{2} - q = m (r - p) \\ y_{2} = m (r - p) + q \\ y_{2} = m r - m p + q \end{array}$

Hence, the unknowny coordinate is $m r - m p + q$ .

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Most popular questions from this chapter

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

17. P(-3, 0); slope = $\frac{2}{5}$ .

In Exercises 28 and 29,

(a) find the lengths of the sides of triangle RST,

(b) use the converse of the Pythagorean Theorem to show that triangle RST is a right triangle, and

(c) find the product of the slopes of RT and ST.

29. R(4, 3), S(-3, 6), T(2, 1)

Find the slope and length of AB.

A(0, -9), B(8, -3)

Write an equation of the circle that has the given center and radius.

$C (0, 0); r = 6$

Name cach line in the figure whose slope is:

a. positive

b. negative

c. zero

d. not defined

See all solutions

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