Answer check please!

[12345678]

‘Find the gradients of the lines joining the following pair of points – (P+Q-1, Q+P-3) and (P-Q+1, Q-P+3)
Gradient (m)= change in y/change in x= (y2-y1)/(x2-x1)
Y2-Y1= Q-P+3-Q+P-3=0
X2-X1= P-Q+1-P+Q-1=0
0/0= error- so how does the textbook come to the answer of (P-3)/(Q-1)?

 

[Deleted member 4993]

‘Find the gradients of the lines joining the following pair of points – (P+Q-1, Q+P-3) and (P-Q+1, Q-P+3)
Gradient (m)= change in y/change in x= (y2-y1)/(x2-x1)
Y2-Y1= Q-P+3-Q+P-3=0
X2-X1= P-Q+1-P+Q-1=0
0/0= error- so how does the textbook come to the answer of (P-3)/(Q-1)?

y₁ = Q + P - 3

y₂ = Q - P + 3

y₂ - y₁ = (Q - P + 3) - (Q + P - 3) = Q - P + 3 - Q - P + 3 = -2*P + 6

Now continue....

 

[12345678]

y₁ = Q + P - 3

y₂ = Q - P + 3

y₂ - y₁ = (Q - P + 3) - (Q + P - 3) = Q - P + 3 - Q - P + 3 = -2*P + 6

Now continue....

X2-X1= (P – Q + 1) – (P + Q – 1)= P – Q + 1 – P + Q – 1 = -2Q + 2
M= -2*P + 6/ -2*Q + 2 = P – 3 / Q – 1 }Thanks for your help!

 

[lookagain]

X2-X1= (P – Q + 1) – (P + Q – 1)= P – Q + 1 – P + Q – 1 = -2Q + 2 \(\displaystyle \ \ \)Incorrect. The work in the middle is wrong. **


M= -2*P + 6/ -2*Q + 2 = P – 3 / Q – 1 } \(\displaystyle \ \ \ \ \) These fractions are incorrect, because you are missing required grouping symbols in them.

There were supposed to be grouping symbols in your first post when you did \(\displaystyle \ y_2 - y_1 \ \ and \ \ x_2 - x_1.\)

But even when Subhotosh Khan explicitly wrote out the grouping symbols as an example for
\(\displaystyle y_2 - y_1, \ \) you failed to show the result of distributing the negative sign
across the second parenthetical expression when you posted your attempt for \(\displaystyle \ x_2 - x_1.\)


Here is what it should be:


\(\displaystyle x_2 - x_1 \)= (P – Q + 1) – (P + Q – 1) = P – Q + 1 – P - Q + 1 = -2Q + 2


M = (-2*P + 6)/(-2*Q + 2)

= [-2(P - 3)]/[-2(Q - 1)]

= (P – 3)/(Q – 1)