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Chapter 13: Q32. (page 534)

A line passes through points (-2, -1) and (4, 3). Where does the line intersect the x-axis? the y-axis?

Short Answer

Expert verified

The required point of intersection of line withx鈭�补虫颈蝉鈥夆赌夆赌塱蝉鈥夆赌�(鈭�12,0)鈥夆赌塧苍诲鈥夆赌�y鈭�补虫颈蝉鈥夆赌塱蝉鈥夆赌�(0,13)

Step by step solution

01

Step-1 – Given

Given that a line passes through points(鈭�2,鈭�1) and(4,3) .

02

Step-2 – To determine

We have tofind the point of intersection of line withx-axis and y-axis.

03

Step-3 – Calculation 

The two-point formula using these two points(x1,y1)鈥夆赌塧苍诲鈥夆赌�(x2,y2) is:

y鈭�y1=y2鈭�y1x2鈭�x1(x鈭�x1)

The given points are (鈭�2,鈭�1)and(4,3) .

y鈭�(鈭�1)=3鈭�(鈭�1)4鈭�(鈭�2)(x鈭�(鈭�2))y+1=23(x+2)3y+3=2x+43y鈭�2x=1

The equation of the x-axis is y = 0, we solve it with3y鈭�2x=1 .

3y鈭�2x=13(0)鈭�2x=1鈭�2x=1x=鈭�12

Equation of the y-axis is x = 0, solving it with3y鈭�2x=1 .

3y鈭�2x=13y鈭�2(0)=13y=1y=13

So, the required point of intersection of line withx鈭�补虫颈蝉鈥夆赌夆赌塱蝉鈥夆赌�(鈭�12,0).

鈥夆赌塧苍诲鈥夆赌�y鈭�补虫颈蝉鈥夆赌塱蝉鈥夆赌�(0,13)

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Most popular questions from this chapter

In Exercises 35-38 find an equation of the circle described and sketch the graph.

The circle has center (-2, -4) and passes through point (3, 8).

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?

If so, which point lies between the other two?

13. A(0, 3), B(-2, 1), C(3, 6)

a. List twelve points, each with integer coordinates, that are 5 units from (-8, 1).

b. Find an equation of the circle containing these points.

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.

P(0, -5); slope =鈭�14.

2. Which of the following points lie on a horizontal line through C?

(2, 4) (2, -4) (0, 4)

(4, 3) (15, 4) (-4, 3)
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