Pack B — Fluency

Mathematics

Year 10 · Coordinate Geometry

Pack B · Fluency

Name: _________________________________

Date: _________________ Class: ___________

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

BronzeQuestions 1–10

1.
Find the midpoint of $A(3, 5)$ and $B(9, 5)$ .
2.
Find the midpoint of $C(4, 3)$ and $D(4, 11)$ .
3.
Find the gradient of the line through $(2, 1)$ and $(5, 10)$ .
4.
Find the gradient of the line through $(2, 10)$ and $(6, 2)$ .
5.
Find the distance between $(4, 5)$ and $(12, 5)$ .
6.
State the $y$ -intercept of the line $y = 2x + -4$ .
7.
State the gradient of the line $y = -3x + 2$ .
8.
A line has gradient $3$ and $y$ -intercept $-1$ . Write the equation of the line.
9.
Does the point $(4, 11)$ lie on the line $y = 3x + -1$ ?
10.
Find $y$ when $x = 5$ on the line $y = -1x + 7$ .

SilverQuestions 11–20

11.
Find the distance between $(2, 3)$ and $(8, 11)$ .
12.
Find the exact distance between $(0, 0)$ and $(2, 5)$ .
13.
Find the midpoint of $(-6, 1)$ and $(4, -7)$ .
14.
Find the gradient of the line through $(-4, 2)$ and $(2, 14)$ .
15.
A line has gradient $2$ and passes through $(4, 3)$ . Find its equation in the form $y = mx + c$ .
16.
Find the equation of the line through $(2, 1)$ and $(5, 10)$ .
17.
A line is parallel to $y = -2x + 3$ . State its gradient.
18.
A line is perpendicular to $y = 3x + -1$ . State its gradient.
19.
Rewrite the equation $3x + 2y = 12$ in the form $y = mx + c$ .
20.
Find the $x$ -intercept of the line $y = 3x + -12$ .

GoldQuestions 21–30

21.
Find the exact distance between $(-1, -2)$ and $(5, 6)$ .
22.
What is the gradient of the line through $(5, 2)$ and $(5, 7)$ ?
23.
Find the equation of the line through $(2, -3)$ that is parallel to the $x$ -axis.
24.
A line passes through $(6, 5)$ and is perpendicular to $y = 3x + -2$ . Find its equation.
25.
The midpoint of $AB$ is $(3, 6)$ where $A = (-1, 2)$ . Find $B$ .
26.
Find the gradient of the line through $(1.5, 2)$ and $(4.5, 11)$ .
27.
Are the points $(1, 2)$ , $(4, 5)$ , and $(7, 8)$ collinear?
28.
Find the equation of the line passing through $(6, 5)$ with gradient $-\dfrac{{m_num}}{{m_den}}$ .
29.
Find the point of intersection of $y = 3x + -2$ and $y = -1x + 6$ .
30.
$ABCD$ is a rectangle with $A(1, 2)$ and $B(4, 8)$ . State the gradient of $CD$ .

PlatinumQuestions 31–40

31.
Find the equation of the perpendicular bisector of $A(1, 2)$ and $B(5, 14)$ .
32.
A triangle has vertices $A(0, 0)$ , $B(8, 0)$ , $C(0, 5)$ . Show that $\triangle ABC$ is right-angled at $A$ .
33.
Show that the triangle with vertices $A(0, 0)$ , $B(6, 0)$ , $C(3, 6)$ is isosceles. Find its area.
34.
The points $(1, 3)$ and $(5, k)$ lie on a line with gradient $-3$ . Find $k$ .
35.
Three vertices of a parallelogram $ABCD$ are $A(1, 1)$ , $B(5, 2)$ , $C(6, 8)$ . 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 $(0, 8)$ and $(6, 0)$ . (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 $B$ .