Form 2 mathematics

Question

In the diagram, PQR is an isosceles triangle on a Cartesian plane. Calculate the area of triangle PQR. Give the answer in two decimal places.

Comments

答案是什么？(●'◡'●)

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51.98 units²

Answer 1

在此之前，先感谢 ୧(＾ 〰 ＾)୨ 版主 给的少许 “线索”，帮助我解开了这题。

如下：



* 补充 ：下面的点是 R，不是 Q，写错了。

谢谢～
 

Comments

三角形的照片你写到2个Q了

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哦，抱歉。

Answer 2

The correct answer should be 52 units², not 51.98 units². ( The workings below is just for references, if your maths teacher mentions to add something, please add it or you may deducted marks,)

Method 1

Let A(-4, 4), B(6, -8), C(-4, -8) be three points on the Cartesian plane. Let us connect AC, CB, BQ, QA to get a rectangle ACBQ and triangle PQR lies inside the rectangle. As the picture as shown below.

 

Now, let us start the calculation:

Method 2

Properties before the answer ( see picture below)

If triangle ABC is an isosceles triangle, where AB=AC, let us draw an altitude from point A to the line BC and meet at D, then we have properties as below:

(i)BD=DC

(ii) angle BAD= angle CAD

(iii) angle ADB= angle ADC= 90 degrees

And we also can conclude that triangle ABD and triangle ACD are congruent.

Back to the question

Comments

额外有趣解法，给回答个赞吧

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现在才发现 三角形 PQR 是等腰直角三角形（那这一题就简单多了），谢谢 @阳光开朗神秘男孩 的回答。

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没事，我们都被外在的物质给误导了，下次要注意。