Pack A — Fluency

Mathematics

Year 10 · Coordinate Geometry

Pack A · Fluency

Name: _________________________________

Date: _________________ Class: ___________

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

BronzeQuestions 1–10

1.
Find the midpoint of $A(2, 4)$ and $B(8, 4)$ .
2.
Find the midpoint of $C(6, 2)$ and $D(6, 10)$ .
3.
Find the gradient of the line through $(1, 3)$ and $(4, 9)$ .
4.
Find the gradient of the line through $(1, 8)$ and $(5, 2)$ .
5.
Find the distance between $(2, 3)$ and $(9, 3)$ .
6.
State the $y$ -intercept of the line $y = 3x + 5$ .
7.
State the gradient of the line $y = 4x + 7$ .
8.
A line has gradient $2$ and $y$ -intercept $5$ . Write the equation of the line.
9.
Does the point $(3, 11)$ lie on the line $y = 2x + 5$ ?
10.
Find $y$ when $x = 4$ on the line $y = 2x + 3$ .

SilverQuestions 11–20

11.
Find the distance between $(1, 2)$ and $(5, 5)$ .
12.
Find the exact distance between $(1, 1)$ and $(4, 5)$ .
13.
Find the midpoint of $(-3, 4)$ and $(5, -2)$ .
14.
Find the gradient of the line through $(-2, 3)$ and $(4, -3)$ .
15.
A line has gradient $3$ and passes through $(2, 5)$ . Find its equation in the form $y = mx + c$ .
16.
Find the equation of the line through $(1, 3)$ and $(4, 9)$ .
17.
A line is parallel to $y = 4x + 7$ . State its gradient.
18.
A line is perpendicular to $y = 2x + 5$ . State its gradient.
19.
Rewrite the equation $2x + 1y = 6$ in the form $y = mx + c$ .
20.
Find the $x$ -intercept of the line $y = 2x + -6$ .

GoldQuestions 21–30

21.
Find the exact distance between $(-3, 2)$ and $(5, -4)$ .
22.
What is the gradient of the line through $(3, 2)$ and $(3, 7)$ ?
23.
Find the equation of the line through $(4, 7)$ that is parallel to the $x$ -axis.
24.
A line passes through $(4, 6)$ and is perpendicular to $y = 2x + 1$ . Find its equation.
25.
The midpoint of $AB$ is $(5, 4)$ where $A = (2, 1)$ . Find $B$ .
26.
Find the gradient of the line through $(0.5, 1.5)$ and $(2.5, 5.5)$ .
27.
Are the points $(1, 2)$ , $(3, 8)$ , and $(5, 14)$ collinear?
28.
Find the equation of the line passing through $(4, 3)$ with gradient $-\dfrac{{m_num}}{{m_den}}$ .
29.
Find the point of intersection of $y = 2x + 1$ and $y = -1x + 7$ .
30.
$ABCD$ is a rectangle with $A(1, 2)$ and $B(5, 5)$ . State the gradient of $CD$ .

PlatinumQuestions 31–40

31.
Find the equation of the perpendicular bisector of $A(1, 2)$ and $B(7, 10)$ .
32.
A triangle has vertices $A(0, 0)$ , $B(6, 0)$ , $C(0, 4)$ . Show that $\triangle ABC$ is right-angled at $A$ .
33.
Show that the triangle with vertices $A(0, 0)$ , $B(6, 0)$ , $C(3, 4)$ is isosceles. Find its area.
34.
The points $(1, 3)$ and $(5, k)$ lie on a line with gradient $2$ . Find $k$ .
35.
Three vertices of a parallelogram $ABCD$ are $A(1, 1)$ , $B(5, 2)$ , $C(7, 6)$ . Find $D$ .
36.
In triangle $ABC$ , $A(0, 0)$ , $B(8, 0)$ , $C(2, 6)$ . Find the equation of the altitude from $C$ to $AB$ .
37.
For what value of $k$ are the points $(1, 2)$ , $(3, k)$ and $(5, 14)$ collinear?
38.
A point $P$ lies on the $x$ -axis and is equidistant from $A(1, 4)$ and $B(7, 2)$ . Find $P$ .
39.
A line passes through $(0, 6)$ and $(4, 0)$ . (a) Find its equation. (b) Find the area of the triangle formed by the line and the axes.
40.
A point $B$ is $5$ units from $A(2, 1)$ along the line $y = 0x + 1$ . Find one possible position of $B$ .