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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

11.2 斜率 Gradient

11.2 Gradient 斜率


 

(1) Given that A(–1, 4), B(2, –3), find the gradient and the angle of inclination of line AB
A(–1, 4), B(2, –3), 求直线AB 的斜率和倾斜角。

Answer:
-\frac{7}{3}, 113^{\circ}12'
2. If points (1, -1), (p, 2) and (p^2, p + 3) are collinear, find the value of p.

若点 (1, -1), (p, 2) 和 (p^2, p + 3) 共线, 求 p 的值。

Answer:
\frac{1}{2}, 1

3.   Prove that (a, 0), (at^2, 2at) and (\frac{a}{t^2},-\frac{2a}{t}) are collinear.

证明 (a, 0), (at^2, 2at) 和 (\frac{a}{t^2},-\frac{2a}{t}) 共线。


 

4. Points P(-1, 11), Q(2, 5) and R(t, 3), given that \anglePQR = 90^{\circ}, find the value of t.
If the line PQ is prolonged to S such that QS = PQ. Find the coordinate of S.

点P(-1, 11), Q(2, 5) 和 R(t, 3), 已知 \anglePQR = 90^{\circ}, 求 t 的值.
若线段PQ 延长到S 使得 QS = PQ. 求S 的坐标.

Answer:
–2, (5, –6 )
5. ABCD is a rhombus that the coordinates of A, B, C and D are (3, 2), (7, p), (q, r) and (2, 6) respectively. Calculate the values of p, q and r.

ABCD 为一菱形且A, B, C 和 D 的坐标分别为 (3, 2), (7, p), (q, r) 和 (2, 6). 计算 p, q 和 r的值。

Answer:
3, 6, 7
6. Prove that (5, 2), (2, 7), (-3, 4) and (0, -1) are the vertices of a square.

证明(5, 2), (2, 7), (-3, 4) 和 (0, -1) 是一正方形的顶点。