Course Content
第四章:部分分式 Partial Fraction
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第六章:角的形成及单位 Angles and Measurements
0/1
第十三章: 方程组 Simultaneous Equations
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第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming
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高中一 | 高级数学
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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。

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