WISKUNDE
GRAAD 10
NOG OEFENINGE
Vergelykings van lyne : antwoorde.
MATHEMATICS
GRADE 10
MORE EXERCISES
Equations of lines : answers.
Antwoord / Answer 1.1
y
B − y
A
m(AB) = ──────
x
B − x
A
12 − 2
= ──────
8 − 3
10
= ─── = 2
5
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
At A / By A : y − 2 = 2(x − 3)
y − 2 = 2x − 6
y = 2x − 6 + 8
y = 2x + 2
Vraag / Question 1.1
Antwoord / Answer 1.2
y
D − y
C
m(CD) = ──────
x
D − x
C
9 − 7
= ──────
5 − 2
2
= ───
3
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
2
By / At C : y − 7 = ─── (x − 2)
3
2 4
y = ───x − ─── + 7
3 3
2 17
y = ───x + ───
3 3
OF / OR 2x − 3y + 17 = 0
Vraag / Question 1.2
Antwoord / Answer 1.3
y
L − y
K
m(KL) = ──────
x
L − x
K
−1 − (−5)
= ────────
−3 − (−8)
4
= ───
5
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
4
By / At K : y − (−5) = ─── (x − (−8))
5
4
y + 5 = ─── x + 8
5
4 7
y = ─── x + ───
5 5
OF / OR 4x − 5y + 7 = 0
Vraag / Question 1.3
Antwoord / Answer 1.4
y
Q − y
P
m(PQ) = ──────
x
Q − x
P
−3 − 7
= ──────
1 − (−6)
−10
= ───
7
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
−10
By / At P : y − 7 = ─── (x − (−6))
7
−10 60
y = ───x − ─── + 7
7 7
−10 11
y = ───x − ───
7 7
OF / OR 10x + 7y + 11 = 0
Vraag / Question 1.4
Antwoord / Answer 1.5
y
S − y
R
m(RS) = ──────
x
S − x
R
−7 − (−12)
= ────────
1 − (−3)
5
= ───
4
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
5
By / At R : y − (−12) = ─── (x − (−3))
4
5 15
y + 12 = ─── x + ───
4 4
5 33
y = ─── x − ───
4 5
OF / OR 5x − 4y − 33 = 0
Vraag / Question 1.5
Antwoord / Answer 1.6
y
B − y
A
m(AB) = ──────
x
B − x
A
−4 − (−8)
= ──────
3 − (−6)
4
= ───
9
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
4
By / At A : y − (−8) = ─── (x − (−6))
9
4 24
y = ───x − ─── − 8
9 9
4 48
y = ───x − ───
9 9
OF / OR 4x − 9y − 48 = 0
Vraag / Question 1.6
Antwoord / Answer 2.1
m = 3
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
By / At A : y − 9 = 3(x − 4)
y = 3x − 12 + 9
y = 3x − 3
Vraag / Question 2.1
Antwoord / Answer 2.2
y = −2x + 5 en dus is / and therefore
m = −2
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
By / At B : y − 7 = −2(x − (−4))
y = −2x − 8 + 7
y = −2x − 1
Vraag / Question 2.2
Antwoord / Answer 2.3
3 3
3x − 4y − 6 = 0
∴
y = ───x − ───
4 2
Die lyne is ewewydig / The lines are parallel
3
∴ m = ──
4
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
3
By / At C : y − (−5) = ── (x − (−4))
4
3
y = ── x + 3 − 5
4
3
y = ── x − 2
4
OF / OR 3x − 4y − 8 = 0
Vraag / Question 2.3
Antwoord / Answer 2.4
2
2x + 3y − 9 = 0
∴
y = − ───x + 3
3
Die lyne is ewewydig / The lines are parallel
2
∴ m = − ──
3
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
2
By / At D : y − (−5) = − ── (x − 3)
3
2
y = − ── x + 2 − 5
3
2
y = − ── x − 3
3
OF / OR 2x + 3y + 9 = 0
Vraag / Question 2.4
Antwoord / Answer 2.5
y = 4x − 3
∴ m = 4
Loodregte lyne / Perpendicular lines :
∴ m
⊥ × 4 = −1
1
∴ m
⊥ = − ──
4
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
1
By / At E : y − 6 = − ── (x − 4)
4
1
y = − ── x + 1 + 6
4
1
y = − ── x + 7
4
OF / OR x + 4y − 7 = 0
Vraag / Question 2.5
Antwoord / Answer 2.6
3 9
3x + 2y − 9 = 0
y = − ── x − ──
2 2
3
∴ m = − ──
2
Loodregte lyne / Perpendicular lines :
3
∴ m
⊥ × − ── = −1
2
2
∴ m
⊥ = ──
3
Die vergelyking word gegee deur /
The equation is given by :
y − y
1 = m(x − x
1)
2
By / At F : y − (−8) = ── (x − (−5))
3
2 10
y = ── x + ── − 8
3 3
2 14
y = ── x − ──
3 3
OF / OR 2x − 3y − 14 = 0
Vraag / Question 2.6