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Chapter 13: Q33. (page 534)

A ine through H(3, 1) and J(5, a) has positive slope and makes a 60掳 angle measured counterclockwise with the positive x-axis. Find the value of a.

Short Answer

Expert verified

The value of a is23+1 .

Step by step solution

01

Step-1 – Given

Given that: A line through points H(3,1)and J(5,a)has positive slope and makes a60掳 angle measured counterclockwise with the positivex鈭�axis .

02

Step-2 – To determine

We have tofind the value ofa.

03

Step-3 – Calculation 

The slope formula with two points(x1,y1)and(x2,y2)is

m=y2鈭�y1x2鈭�x1

The given points areH(3,1)and J(5,a).

We know that, the slope of a line is defined as 鈥渢he tangent of the angle which the line makes with positive direction of thex鈭�axisin the anticlockwise direction鈥�.

It meansm=tan胃

So,

tan胃=y2鈭�y1x2鈭�x1tan60鈭�=a鈭�15鈭�33=a鈭�12a=23+1

Hence, the value of a is23+1 .

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Most popular questions from this chapter

In Exercises 4-9 state:

a. the coordinates of T.

b. the lengths of the legs of the right triangle.

c. the length of the segment shown.

Use the distance formula to find the distance between the two points.

  1. (3, 2) and (5, -2)

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

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

A wheelchair ramp is to be built at the town library. If the entrance to the library is 18 in. above ground, and the slope of the ramp is, how far out from the building will the ramp start?

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)
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