Advanced problem solving with linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

Two lines are perpendicular if their gradients are the negative __________ of one another.

gradient

multiplier

product

reciprocal ✓
Match each line with a line that is perpendicular to it.

$y=3x-8$

⇔

$y=-{1\over3}x-11$ ✓

$y={1\over2}x+8$

⇔

$y=10-2x$ ✓

$y=7-{2\over3}x$

⇔

$y={3\over2}x-3$ ✓

$y={3\over2}x-10$

⇔

$y=-{2\over3}x+8$ ✓
What is the equation of this line?

$y=1+3x$

$y=1+{1\over3}x$

$y={1\over3}x-1$

$y=-{1\over3}x-1$

$y=1-{1\over3}x$ ✓
What is the equation of the straight line that goes through the coordinates (-5, -23) and (3, 17)?

$y=2-5x$

$y=2x+5$

$y=5x+2$ ✓

$y=5x-2$

$y=2x-5$
Find the coordinates of the point P when AP : PB is in the ratio 1 : 5.

(3, 2)

(2, 3)

(4 3)

(3, 5) ✓

(1, 5)
What is the coordinate of C when AB : BC is in the ratio 1 : 2?

(0.5, 1)

(5, -8)

(7, -12)

(11, -20) ✓

(15, -28)

In a circle, a tangent and a __________ meet at a right angle.

chord

circumference

radius ✓
The grid shows a circle, its radius and a tangent which touches the circumference at (3, -4). What is the equation of the tangent line?

$y=2x+5$

$y=2x-10$ ✓

$y=2x-4$

$y={1\over2}x+5$

$y={1\over2}x-10$
The grid shows a circle, its radius and a tangent which touches the circumference at (3,-4). The radius is a line segment of the line ...

$y=-5-2x$

$y=-2x-2.5$

$y=-{1\over2}x-5$

$y=-{1\over2}x+{5\over2}$

$y=-{1\over2}x-{5\over2}$ ✓
$In this graph the radius is a line segment of the line <Math>y=-{1\over2}x-{5\over2}</Math> and the tangent is line <Math>y=2x-10</Math>. How can you tell they meet at a right angle?$

In this graph the radius is a line segment of the line $y=-{1\over2}x-{5\over2}$ and the tangent is line $y=2x-10$ . How can you tell they meet at a right angle?

$(-4)=-{1\over2}(3)-{5\over2}$

$(-4)=2(3)-10$

$-{5\over2}\times{10}=-25$

$-{1\over2}\times{2}=-1$ ✓

$-{1\over2}\times{2}=1$
Point P is such that AP : PB is in the ratio 1 : 2. Find the area of triangle OPB.

18 sq units

27 sq units

36 sq units ✓

54 sq units
Point P is such that AP : PB is in the ratio 5 : 1. The area of triangle OAP is ______ square units.

'45' ✓

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P is a point such that AP : PB is in the ratio of 1 : 3 means that point P is a third of the distance of AB from A.

There are 4 equal parts in total, meaning that point P is a quarter of the distance of AB from A.

Tangent (of a circle) - The tangent (of a circle) is a line that intersects the circle exactly once.