Question

10. The coordinates of the vertices of region bounded by lines 3x - y -5;x+ 2y 4 and Y-axis are: AV-axis - 284 X-axis B (a) A(2,0); B(5,0) and C(1,2) (c) A(0,2); B(0,-5) and C(2,1) (b) A(2,0); B(-5,0) and C(1,2) (d) A(0,2), B(0,5) and C(2,1) 11 111​

Answer 1

Answer:

I, ~ 3] COORDINATES 3

3. Ratio of Division. A segment AB (Fig. 2) of a straight

line being given, it is shown in elementary geometry how to

find the point C that divides

A C B

AB in a given ratio k. Thus, /

if k =, the point C such.that D /

A0C 2

AB S -5

FIG. 2

is found as follows. On any

line through A lay off AD = 2 and AE= 5; join B and E.

Then the parallel to BE through D meets AB at the required

point C.

Analytically, the problem of dividing a line in a given ratio

is solved as follows. On the line AB (Fig. 3) we choose a

point 0 as origin and assign a positive sense. Then the

abscissas x1 of A and x2 of B are known. To find a point C!<- jc --- —- ^c |

FIG. 3

which divides AB in the ratio of division ic = AC/AB, let us

denote the unknown abscissa of C by x. Then we have

AC= x - x, AB = - xI;

hence the abscissa x of C must satisfy the condition

X- 1,

X2 - X1

whence

x = X1 + k (X2 - X)

or, if we write Ax (read: delta x) for the "difference of the

x'S,"' i.e. Ax = X -X,

x = Xl+ - Ax.

Thus, if the abscissas of A and B are 2 and 7, the abscissas

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Step-by-step explanation:

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Answer 2

Answer:

B(0,5)

Step-by-step explanation:

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