About Lesson
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:
![Rendered by QuickLaTeX.com -\frac{7}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-35667a1c3781fe8ce3f4a5fc980505ae_l3.png)
![Rendered by QuickLaTeX.com 113^{\circ}12'](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1bb886a795027a33a8191a7413951192_l3.png)
2. If points (1, -1), (p, 2) and (
,
) are collinear, find the value of p.
![Rendered by QuickLaTeX.com p^2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-eae84fbcf18d219fc28c53f7ef000710_l3.png)
![Rendered by QuickLaTeX.com p + 3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-e5db11daf23a8473ec68303a120c09a7_l3.png)
若点 (1, -1), (p, 2) 和 (,
) 共线, 求 p 的值。
Answer:
![Rendered by QuickLaTeX.com \frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f5ac0f658c5eea95b9d59561e1d0ecab_l3.png)
![Rendered by QuickLaTeX.com 1](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7297ed5d8a0649a927d31ac326d7d575_l3.png)
3. Prove that (a, 0), (, 2at) and
are collinear.
证明 (a, 0), (, 2at) 和
共线。
4. Points P(-1, 11), Q(2, 5) and R(t, 3), given that PQR = 90
, 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 PQR = 90
, 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。