Pack A — Fluency

Mathematics

Year 9 · 9.5 Coordinate Geometry

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10

1.
State the gradient $m$ and the $y$ -intercept $c$ of the line $y = 3x + 2$ .
2.
Find the gradient of the line through $(1, 2)$ and $(4, 8)$ .
3.
Find the midpoint of the segment from $(2, 4)$ to $(8, 10)$ .
4.
Find the distance between $(0, 0)$ and $(3, 4)$ .
5.
A line parallel to $y = 4x + 7$ . Find its gradient.
6.
A line perpendicular to $y = 2x + 3$ . Find its gradient.
7.
Complete the table of values for $y = 2x + 1$ at $x = -1, 0, 1, 2$ .
8.
Write the equation of the line with gradient 3 and $y$ -intercept -4.
9.
State the equation of the horizontal line through $(2, 7)$ and the vertical line through $(-3, 5)$ .
10.
Find the $x$ - and $y$ -intercepts of $y = 3x + 6$ .

SilverQuestions 11–20

11.
Find the gradient through $(3, 8)$ and $(7, 2)$ .
12.
Find the distance between $(1, 1)$ and $(4, 5)$ as a simplified surd.
13.
Find the equation of the line through $(1, 3)$ and $(3, 7)$ .
14.
Find the equation of the line parallel to $y = 2x + 3$ passing through $(1, 4)$ .
15.
Find the equation of the line perpendicular to $y = 2x + 1$ through $(4, 3)$ .
16.
Find the midpoint of $A(-4, 3)$ and $B(6, -7)$ with mixed signs.
17.
Find the equation of the line with gradient 3 through $(2, 1)$ .
18.
Decide parallel / perpendicular / neither: (a) $y = 3x + 2$ and $y = 3x - 5$ . (b) $y = 4x + 1$ and $y = -x/4 + 5$ .
19.
Find the equation of the line perpendicular to $y = (1/3)x + 2$ passing through $(3, 1)$ .
20.
Find the equation of the line through (2, 4) and (5, 4).

GoldQuestions 21–30

21.
A line passes through $A(-2, 1)$ and $B(7, 4)$ . Find its equation.
22.
The point C divides AB in ratio 2:1, $A(-2, 1)$ , $B(7, 4)$ . Find C.
23.
Find the equation of the perpendicular bisector of A(1, 2) and B(5, 6).
24.
Find the $x$ - and $y$ -intercepts of $3x + 4y = 12$ .
25.
Does the point (3, 7) lie on the line $y = 2x + 1$ ? Justify.
26.
Find the equation of the line parallel to $2x + 3y = 6$ passing through $(0, 0)$ .
27.
Find the perimeter of triangle $A(0, 0)$ , $B(4, 3)$ , $C(8, 0)$ .
28.
A line $\ell_1$ has equation $y = mx + 2$ . It is perpendicular to $\ell_2: y = (1/4)x + 5$ . Find $m$ .
29.
Find the foot of the perpendicular from $P(5, 1)$ to the line $y = 2x - 1$ .
30.
A line through $(1, 5)$ is parallel to a line through $(0, 1)$ and $(4, 9)$ . Find its equation.

PlatinumQuestions 31–40

31.
A triangle has vertices A(1, 2), B(7, 4), C(4, 10). (a) Find the midpoint M of BC. (b) Find the equation of the median from A.
32.
Show that points P(-1, -3), Q(2, 3), R(5, 9) are collinear.
33.
Find the perpendicular distance from $P(5, 1)$ to the line $y = 2x - 1$ .
34.
A line passes through $(a, 0)$ and $(0, b)$ . Find its equation.
35.
Find the area of the triangle bounded by $y = x + 1$ , $y = -x + 5$ , $y = 0$ .
36.
A triangle has vertices $A(0, 0), B(4, 2), C(1, 5)$ . Verify whether it is right-angled.
37.
The point M(3, 2) is the midpoint of AB, where A = (1, 5). Find B.
38.
A quadrilateral has vertices A(0, 0), B(4, 0), C(5, 3), D(1, 3). Find the gradients of all 4 sides and identify the shape.
39.
Find the value of $k$ for which the lines $y = 2x + k$ and $y = 3x + 1$ intersect at a point on the $x$ -axis.
40.
The line $\ell$ has equation $3x - 4y = 12$ . Find (a) the slope, (b) the $x$ - and $y$ -intercepts, (c) the perpendicular distance from origin to $\ell$ .