Question

1) What is the equation of line CD?if C(9,4) and D(6,1). (i) x-y-5=0 (ii)x+y-5=0. (iii)x+y+5=0. (iv)x-y+5=0​

Answer 1

Question :- What is the equation of line CD ? if C(9,4) and D(6,1).

(i) x-y-5=0

(ii)x+y-5=0

(iii)x+y+5=0

(iv)x-y+5=0

Solution :-

we know that,

• Slope of a line , when points of line are (a,b) and (c,d) is = (d - b) / (c - a)
• Equation of line with slope m = y - y1 = m(x - x1).

given that,

• a = 9 = x1
• b = 4 = y1
• c = 6
• d = 1

so,

→ slope of line , m = (1 - 4) / (6 - 9) = (-3)/(-3) = 1

then,

→ Equation of line :- y - y1 = 1(x - x1)

→ Equation of line :- y - 4 = 1(x - 9)

→ Equation of line :- (y - 4) = (x - 9)

→ Equation of line :- x - y - 9 + 4 = 0

→ Equation of line :- x - y - 5 = 0 (i) (Ans.)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The equation of line CD if C(9,4) and D(6,1)

(i) x-y-5=0

(ii) x+y-5=0

(iii) x+y+5=0

(iv) x-y+5=0

EVALUATION

Here the given points are C(9,4) and D(6,1)

So the required equation of the line CD is

$\displaystyle \sf{ \frac{y - 4}{x - 9} = \frac{4 - 1}{9 - 6} }$

$\displaystyle \sf{ \implies \frac{y - 4}{x - 9} = \frac{3}{3} }$

$\displaystyle \sf{ \implies \frac{y - 4}{x - 9} = 1 }$

$\displaystyle \sf{ \implies y - 4 = x - 9 }$

$\displaystyle \sf{ \implies x -y - 5 = 0 }$

FINAL ANSWER

The correct option is

$\displaystyle \sf{ x -y - 5 = 0 }$

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