kai ki
Lv 5
kai ki 發問於 科學及數學數學 · 1 十年前

F3 to F4 Maths coordinate geometry of straight lines

Prove that the straight line passing though A(2,3) and B(-4,-6) passes through the origin.

I do not understand what answer do the question want?

thanks....

2 個解答

• 1 十年前
最愛解答

Prove that the straight line passing though A(2,3) and B(-4,-6) passes through the origin.

I do not understand what answer do the question want?

first, we need to find the slope

slope = 3+6/2+4 = 9/6 = 3/2

then , we find the equation of this straight line

by the formula y-y(1) = m[x-x(1)]

equation = y-3 = 3/2(x-2)

y-3 = 3/2(x-2)

2y - 6 = 3x - 6

2y-3x=0

the eqaution of the straight line : 2y-3x=0

put x = 0 into the equation 2y-(3)(0) = 0 , y= 0

when x=0, y=0, so line is pass through the origin

2008-08-22 20:53:57 補充：

Prove that the straight line passing though A(2,3) and B(-4,-6) passes through the origin.

其實我同上面都用左附加數方法

正確中三用的方法

應該用斜率計

同一正線上, 任何兩點的斜率都會一樣

即係我地計左成條斜率係3/2

再計A點同O點的斜率, 又係3/2

再計B點同O點的斜率, 都係3/2

即係A,O,B,3點係同一條線

• Ellen
Lv 6
1 十年前

equation of the straight line passing though A(2,3) and B(-4,-6) is:

(y-3)/(x-2)=(-6-3)/(-4-2)

(y-3)/(x-2)=-9/-6

2(y-3)=3(x-2)

2y-6=3x-6

3x-2y=0

put O(0,0) into 3x-2y=0

3(0)-2(0)=0

it satisfies the equation that means the line 3x-2y=0 passes through the origin.