In 5 years' time, Kate's father will be 3 times as old as Kate. Four years ago, her father was 6 times as old as her. Find their present ages.

Kate = 40/3  Her father = 50

Step-by-step explanation:

Let Kate's age in the present be K

And Kate's father's age in the present be F

3(K+5) = F+5

6(K-6) = F-6

Rearrange the first equation to get

3K+15 = F+5

3K+10 = F

Substitute that into the second question

6K-36 = 3K+10-6

3K = 40

K = 40/3

So F = 3*40/3+10 = 50

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.