The point `C(-2,3)` is the midpoint of the interval `AB`, where `B` has coordinates `(-1,0).`
What are the coordinates of `A`? (3 marks)
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The point `C(-2,3)` is the midpoint of the interval `AB`, where `B` has coordinates `(-1,0).`
What are the coordinates of `A`? (3 marks)
`(-3,6)`
`text(Using the midpoint formula):`
`(x_A + x_B)/2` | `= x_C` | `(y_A + y_B)/2` | `= y_C` |
`(x_A-1)/2` | `= -2` | `(y_A + 0)/2` | `= 3` |
`x_A` | `= -3` | `y_A` | `= 6` |
`:. A\ text(has coordinates)\ (-3,6).`
Given `C(-3,-5)` and `D(-5,1)`, find the midpoint of `CD`. (2 marks)
`(-4, -2)`
`C(-3,-5),\ \ \ D(-5,1)`
`M` | `= ( (x_1 + x_2)/2, (y_1 + y_2)/2)` |
`= ( (-3-5)/2, (-5+1)/2)` | |
`= (-4, -2)` |
Find `M`, the midpoint of `PQ`, given `P(2, -1)` and `Q(5, 7)`. (2 marks)
`M(7/2, 3)`
`P(2,-1)\ \ \ Q(5,7)`
`M` | `= ( (x_1 + x_2)/2, (y_1 + y_2)/2)` |
`= ( (2+5)/2, (-1+7)/2)` | |
`= (7/2, 3)` |
The point `R(9, 5)` is the midpoint of the interval `PQ`, where `P` has coordinates `(5, 3).`
What are the coordinates of `Q`?
`C`
`text(Using the midpoint formula):`
`(x_Q + x_P)/2` | `= x_R` | `(y_Q + y_P)/2` | `= y_R` |
`(x_Q + 5)/2` | `= 9` | `(y_Q + 3)/2` | `= 5` |
`x_Q` | `= 13` | `y_Q` | `= 7` |
`:. Q\ text(has coordinates)\ (13, 7).`
`=> C`
Let `M` be the midpoint of `(-1, 4)` and `(5, 8)`.
Find the equation of the line through `M` with gradient `-1/2`. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`x + 2y-14 = 0`
`(-1,4)\ \ \ (5,8)`
`M` | `= ( (x_1 + x_2)/2, (y_1 + y_2)/2)` |
`= ( (-1 + 5)/2, (4 + 8)/2)` | |
`= (2, 6)` |
`text(Equation through)\ (2,6)\ text(with)\ m = -1/2`
`y-y_1` | `= m (x-x_1)` |
`y-6` | `= -1/2 (x-2)` |
`2y-12` | `= -x + 2` |
`x + 2y-14` | `= 0` |