Akal Pintar

边的方向 = arah sisi 先把已知的三个点画在方格上。P 和 Q 的第二个数字都是 1，所以 PQ 是一条横边，长 3 格；Q 和 R 的第一个数字都是 4，所以 QR 是一条竖边，也是 3 格。正方形对面的边互相平行，所以第四个顶点要和 R 在同一条横线上，和 P 在同一条竖线上。 例子：(2, 5) 和 (6, 5) 的第二个数字相同，它们在同一条横线上。 注意：第二个数字相同 → 横线；第一个数字相同 → 竖线。

direction of the sides = arah sisi First plot the three known points. P and Q both have second number 1, so PQ is a horizontal side 3 units long; Q and R both have first number 4, so QR is a vertical side, also 3 units. Opposite sides of a square are parallel, so the fourth vertex must be on the same horizontal line as R and the same vertical line as P. Example: (2, 5) and (6, 5) have the same second number, so they are on the same horizontal line. Watch out: same second number → horizontal line; same first number → vertical line.

借用两个数字 = pinjam dua nombor K 在 P 的正上方，所以 K 的第一个数字和 P 一样；K 和 R 在同一条横线上，所以 K 的第二个数字和 R 一样。把这两个数字合起来，就是 K 的坐标 (1, 4)。 例子：一个长方形三个顶点是 (2, 2)、(5, 2)、(5, 6)，第四个顶点借 (2, 2) 的第一个数字和 (5, 6) 的第二个数字。 注意：不要把三个点的数字随便加减，要看哪一个点和 K 同一条线。

borrow two numbers = pinjam dua nombor K is straight above P, so K's first number is the same as P's; K is on the same horizontal line as R, so K's second number is the same as R's. Put the two numbers together and K is at (1, 4). Example: if a rectangle has vertices (2, 2), (5, 2) and (5, 6), the fourth vertex takes the first number of (2, 2) and the second number of (5, 6). Watch out: do not just add or subtract the numbers; look at which point shares a line with the missing vertex.

验算边长 = semak panjang sisi 横边的长度看第一个数字相差多少，竖边的长度看第二个数字相差多少。四条边都算一次：都是 3 格，四条边一样长，四个角都是直角，所以找到的 K 是对的。 例子：从 (2, 3) 到 (2, 7) 的竖边，长 7 − 3 = 4 格。 注意：如果有一条边长度不同，K 就找错了，要重新检查。

check the side lengths = semak panjang sisi For a horizontal side, find the difference between the first numbers; for a vertical side, the difference between the second numbers. Work out all four sides: each is 3 units, all equal, with four right angles, so the K we found is correct. Example: the vertical side from (2, 3) to (2, 7) is 7 − 3 = 4 units long. Watch out: if any side has a different length, K is wrong and you must check again.

缺少的顶点 = bucu yang tiada 先找出缺的顶点和哪一个已知点在同一条竖线上，它的第一个数字就借那一个点；再找出它和哪一个已知点在同一条横线上，第二个数字就借那一个点。最后数一数四条边是不是一样长。 例子：正方形三个顶点 (1, 1)、(3, 1)、(1, 3)，缺的顶点借 (3, 1) 的第一个数字和 (1, 3) 的第二个数字。 注意：可以先把三个点画在方格上，再看缺的角在哪里。

the missing vertex = bucu yang tiada Find which known point shares a vertical line with the missing vertex; its first number is borrowed from that point. Then find which known point shares a horizontal line with it; its second number is borrowed from that one. Finally check that all four sides are equal. Example: for a square with vertices (1, 1), (3, 1) and (1, 3), the missing vertex takes the first number of (3, 1) and the second number of (1, 3). Watch out: you can plot the three points first to see which corner is missing.

长方形的第四个顶点 = bucu keempat segi empat tepat 长方形和正方形一样，对边平行，边是横的或竖的，只是长边和短边不一样长。先看缺的顶点在哪一个已知点的正下方或正上方，借它的第一个数字；再看和哪一个已知点在同一条横线上，借它的第二个数字。 例子：长方形 (0, 1)、(4, 1)、(4, 3)，缺的顶点是 (0, 3)。 注意：长方形的长和宽不一定一样，所以不能用“四边一样长”来检查，要检查对边一样长。

the fourth vertex of a rectangle = bucu keempat segi empat tepat A rectangle, like a square, has parallel opposite sides that are horizontal or vertical; only its long and short sides differ. See which known point the missing vertex is directly above or below, and borrow its first number; then see which known point shares its horizontal line, and borrow its second number. Example: for the rectangle (0, 1), (4, 1), (4, 3), the missing vertex is (0, 3). Watch out: a rectangle's length and width can differ, so check that opposite sides are equal rather than all four.