AMC8 2024

AMC8 2024 · Q11

AMC8 2024 · Q11. It mainly tests Area & perimeter, Coordinate geometry.

The coordinates of $\triangle ABC$ are $A(5,7)$, $B(11,7)$, and $C(3,y)$, with $y>7$. The area of $\triangle ABC$ is 12. What is the value of $y$?

\triangle ABC 的坐标为 $A(5,7)$，$B(11,7)$，和 $C(3,y)$，其中 $y>7$。\triangle ABC 的面积为 12。$y$ 的值为多少？

(A) 8 8

(B) 9 9

(D) 11 11

(E) 12 12

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since the triangle has a base of $6$, we can plug in that value as the base. Then, we can solve the equation for the height. Doing so gives us, \[\dfrac{6h}{2}=3h=12.\] This means that $h=4$, so that means that we have to add 4 to the $y$-coordinate. So the answer is $7+4=\boxed{(D) 11}$

由于三角形底边长为 $6$，我们可以将该值代入作为底边。然后，解高度 $h$ 的方程。如此得到， \[\dfrac{6h}{2}=3h=12.\] 这意味着 $h=4$，所以需要将 $y$ 坐标加 4。因此答案为 $7+4=\boxed{(D) 11}$

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