Problem with translation

Geometry Level 3

Points $A(2, 2016)$ and $B(7, 2016)$ form a triangle with the third point $C(X_{C}, Y_{C})$ . The triangle's area is $20$ . If point $C$ is translated by vector $v(2016, 4)$ into point $C'$ , what will be the area of $\triangle ABC'$ ?

Also, it is known that $Y_{C} > 2016$ and $X_{C} < 2016$ .

30 50 20 40 2016 25

1 solution

Milan Milanic
Jan 11, 2016

Solution:

Distance between points $A$ and $B$ is $5 (a)$ . Therefore, trinagle's height on $a$ is $8 (h)$ . When point $C$ is translated, $h$ increases by $4$ (we know that thanks to condition $Y_{C} > 2016$ ). Now, the area will be $\frac{a \times h'}{2} = \frac{5 \times 12}{2} = 30$ .

Problem with translation

1 solution

0 pending reports