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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 slopem passes through pointsp,qandr,mr鈭�mp+q

Step by step solution

01

Step-1 – Given

A line with slopem passes through pointsp,qandr,?

02

Step-2 – To determine

We have tofind the unknowny coordinate of the given point.

03

Step-3 – Calculation 

The slope formula for two pointsx1,y1andx2,y2is:

m=y2鈭�y1x2鈭�x1

The given points are p,qandr,?.

Let = the unknown x coordinate

So,

m=y2鈭�y1x2鈭�x1m=y2鈭�qr鈭�py2鈭�q=mr鈭�py2=mr鈭�p+qy2=mr鈭�mp+q

Hence, the unknowny coordinate is mr鈭�mp+q.

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Most popular questions from this chapter

Find the slope of the line through the points named. If the slope is not defined, write not defined.

(6, -6); (-6, -6)

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.

P(-1, 3) Q(2, 7) R(8, 15)

This exercise provides a geometric method of justifying the fact that you can use any two points on a line to determine the slope of the line. Horizontal and vertical segments have been drawn as shown. Supply the reason for each step.

Key steps of proof:

1.鈥�鈭�B鈮�鈭�A2.鈥�鈭�1鈮�鈭�23.鈥�螖LBN~螖DAJ4.鈥�BNAJ=LBDA,鈥�or鈥�BNLB=AJDA

5. The slope of LN equalsBNLB and the slope of DJ equalsAJDA

6. Slope of LN equals to slope of DJ.

3. Find OD and BF.

What is the x-coordinate of every point that lies on a vertical line through C?
See all solutions

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