Question

Question #1aec1

Answer 1

`K` has co-ordinates of `(11, 16)`

Explanation:

Because `M` is the mid point of a straight line, the changes between the end point `J` and `M` must be the same as the changes between `M` and the end point `K`

The change in the `x` co-ordinate between `J` and `M` is `3 (8-5)`
Therefore the change in `x` from `M` to `K` must also be `3` so `K` has an `x` coordinate of `11 (8 + 3)`

The change in the `y` co-ordinate between `J` and `M` is `11 (5--6)`
Therefore the change in `y` from `M` to `K` must also be `11` so `K` has an `y` coordinate of `16 (5 + 11)`

`K` has co-ordinates of `(11, 16)`

Answer 2

`(7,3)to(B)`

Explanation:

`"2"`

`"questions of this type are best calculated using the"`

`color(blue)"Section formula"`

`"given a line segment say AB that has to be split in the"`
`"ratio m:n"`

`"if "A(x_1,y_1)" and "B(x_2,y_2)`

`"then the coordinates of the point splitting AB in ratio m:n"`
`"are found as follows"`

`•color(white)(x)[(mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)]`

`"here "(x_1,y_1)=(1,3)" and "(x_2,y_2)=(15,3)`

`"and "m:n=3:4`

`rArr(((3xx15)+(4xx1))/(3+4),((3xx3)+(4xx3))/(3+4))`

`=(49/7,21/7)=(7,3)to(B)`