第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

11.1 直角坐标系 Cartesian System Coordinate

11.1 Cartesian System Coordinate 直角坐标系


 

(1) Find the possible values of m if the distance between P(3, m) and Q(0, 2) is 5.

m 所有值,若 P(3, m) 和 Q(0, 2) 之间的距离是 5.

Answer:

6, -2

(2) Given that P(h, 3), Q(-2, 1) and R(3, 2). Calculate all the possible values of h if distance of PQ is twice of the distance of QR.

已知P(h, 3), Q(-2, 1) 和 R(3, 2). 求 h 的所有若 PQ 的距离是 QR距离的两倍.

Answer:

-12, 8

(3) A(a, 3), B(1, -1), C(-2, b) and D(0, 2) are the vertices of a parallelogram. Find the values of a and b.

A(a, 3), B(1, -1), C(-2, b) 和 D(0, 2) 是一个平行四边形的顶点. 求 a 和 b之值.

Answer:

3, -2

(4) A(2, -3), B(h, k) and C(-3, 4) three points are located at the same straight line such that 5AB = 2BC. Find the values of h and k.

A(2, -3), B(h, k) 和 C(-3, 4) 三点在一条线上的点且5AB = 2BC. 求 h 和 k的.

Answer:
\frac{4}{7}, -1

(5) Points A(4, 9), B(-1, -3) and C(-8, 4), show that AB = AC.
If P(a, b) is a point which has the same distance from B and C, prove that a = b – 5.

点A(4, 9), B(-1, -3) 和 C(-8, 4), 求show that 证AB = AC。
若P(a, b) 为一点其与 B 和 C的距离相同, 证 a = b – 5.


 

(6) The distance from (-a, a) to the midpoint of P(-3, -3) and Q(-7, -7) is 10 units, find the value of a.

从(-a, a) 到 P(-3, -3) 和 Q(-7, -7) 的中点的距离是10 单位长, 求 a之值.

Answer:
5
(7) Show that A(-2, -3), B(1, 2) and C(11, -4) is a right angle triangle and state the right angle.

证明A(-2, -3), B(1, 2) 和 C(11, -4) 为一直角三角形并列出那个是直角。

Answer:
B