P(−6 ; 1), Q(2 ; −7) en R(8 ; −1) is die hoekpunte
van ΔPQR.
3.1 Bereken die koördinate van S, die
middelpunt van PQ.
Ant. / Ans. 3.1
3.2 Bepaal die vergelyking van die
swaartelyn/mediaan van R na PQ.
Ant. / Ans. 3.2
3.3 Bereken die gradiënt van RQ.
Ant. / Ans. 3.3
3.4 Watter soort driehoek is ΔPQR?
Gee 'n rede.
Ant. / Ans. 3.4
P(−6 ; 1), Q(2 ; −7) and R(8 ; −1) are the vertices
of ΔPQR.
3.1 Calculate the coordinates of S, the
midpoint of PQ.
Ant. / Ans. 3.1
3.2 Find the equation of the median from
R to PQ.
Ant. / Ans. 3.2
3.3 Calculate the gradient of RQ.
Ant. / Ans. 3.3
3.4 What kind of triangle is ΔPQR?
Give a reason.
Ant. / Ans. 3.4
K(2 ; 9), L(−5 ; −5) en M(−13 ; −1) is die hoekpunte
van ΔKLM.
Toon dat ΔKLM 'n reghoekige driehoek is.
K(2 ; 9), L(−5 ; −5) and M(−13 ; −1) are the vertices
of ΔKLM.
Show that ΔKLM is a right-angled triangle.
D(5 ; 9), E(−3 ; 5) en F(−1 ; 1) is die hoekpunte
van ΔDEF.
Toon dat ∠DEF = 90°.
D(5 ; 9), E(−3 ; 5) and F(−1 ; 1) are the vertices
of ΔDEF.
Show that ∠DEF = 90°.
A(−6 ; 7), B(1 ; −3) enC(−9 ; −10) is die hoekpunte
van ΔABC.
Toon dat ΔABC 'n gelykbenige driehoek is.
A(−6 ; 7), B(1 ; −3) enC(−9 ; −10) are the vertices
of ΔABC.
Show that ΔABC is an isosceles triangle.
P(−3 ; −2), Q(−7 ; 7) en R(2 ; 3) is die hoekpunte
van ΔPQR.
Toon dat ∠QPR = ∠PRQ.
P(−3 ; −2), Q(−7 ; 7) and R(2 ; 3) are the vertices
of ΔPQR.
Show that ∠QPR = ∠PRQ.
A(−2 ; 3), B(−4 ; −1) en C(3 ; −2) is die hoekpunte
van ΔABC en D is die punt (3 ; −2).
9.1 Toon aan dat CD ⊥ AB.
Ant. / Ans. 9.1
9.2 Bepaal die vergelyking van die mediaan
van B na AC.
Ant. / Ans. 9.2
9.3 Bereken die oppervlakte
van ΔABC.
Ant. / Ans. 9.3
A(−2 ; 3), B(−4 ; −1) and C(3 ; −2) are the vertices
of ΔABC and D is the point (3 ; −2).
9.1 Show that CD ⊥ AB.
Ant. / Ans. 9.1
9.2 Find the equation of the median
from B to AC.
Ant. / Ans. 9.2
9.3 Calcualte the area of ΔABC.
Ant. / Ans. 9.3
Die figuur toon vierhoek ABCD met hoekpunte
A(−1 ; 4), B(−4 ; 1), C(−1 ; −2) en D(3 ; 2).
10.1 Toon dat AB || CD.
Ant. 10.1
10.2 Toon aan dat AB = CD.
Ant. 10.2
10.3 Bepaal die grootte van ∠ABC.
Ant. 10.3
10.4 Sê, met redes, watter soort
vierhoek ABCD is.
Ant. 10.4
The figure shows quadrilateral ABCD with vertices
A(−1 ; 4), B(−4 ; 1), C(−1 ; −2) and D(3 ; 2).
10.1 Show that AB || CD.
Ans. 10.1
10.2 Show that AB = CD.
Ans. 10.2
10.3 Calculate the size of ∠ABC.
Ans. 10.3
10.4 Say, with reasons, what kind
of quadrilateral ABCD is.
Ans. 10.4
Die figuur toon vierhoek KLMN met hoekpunte
K(1 ; 5), L(−3 ; −1), M(−1 ; −3) en N(3 ; 3).
11.1 Toon dat KN || LM.
Ant. 11.1
11.2 Toon aan dat KN = LM.
Ant. 11.2
11.3 Is KLMN 'n reghoek?
Gee 'n rede.
Ant. 11.3
The figure shows quadrilateral KLMN with vertices
K(1 ; 5), L(−3 ; −1), M(−1 ; −3) and N(3 ; 3).
11.1 Show that KN || LM.
Ans. 11.1
11.2 Show that KN = LM.
Ans. 11.2
11.3 Is KLMN a rectangle?
Give a reason.
Ans. 11.3
Die figuur toon vierhoek PQRS met hoekpunte
P(2 ; 5), Q(−4 ; 1), R(−3 ; −2) en S(3 ; 2) .
12.1 Bereken die koördinate van M, die
middelpunt van PR.
Ant. / Ans. 12.1
12.2 Toon aan dat QM = MS.
Ant. / Ans. 12.2
12.3 Bereken die gradiënt van QR en
van RS.
Ant. / Ans. 12.3
12.4 Sê, met redes, watter soort
vierhoek PQRS is.
Ant. / Ans. 12.4
The figure shows quadrilateral PQRS with vertices
P(2 ; 5), Q(−4 ; 1), R(−3 ; −2) and S(3 ; 2)
12.1 Calculate the coordinates of M the
midpoint of PR.
Ant. / Ans. 12.1
12.2 Show that QM = MS.
Ant. / Ans. 12.2
12.3 Calculate the gradient of QR and of RS.
Ant. / Ans. 12.3
12.4 Say, giving reasons, what kind of quadrilateral
PQRS is.
Ant. / Ans. 12.4
P(−2 ; 2), Q(1 ; −1), R(4 ; 2) en S(2 ; a) is die
hoekpunte van vierhoek PQRS. Bereken a se
waarde as PS || QR.
P(−2 ; 2), Q(1 ; −1), R(4 ; 2) and S(2 ; a) are
the vertices of quadrilateral PQRS. Calculate the
value of a if PS || QR.
K(−2 ; 3), L(2 ; 6), en M(5 ; 2) is die hoekpunte
van driehoek KLM.
15.1 Bewys dat ΔKLM 'n gelykbenige, reghoekige
driehoek is.
15.2 Bereken die oppervlakte van ΔKLM.
K(−2 ; 3), L(2 ; 6), and M(5 ; 2) are the vertices
of triangle KLM.
15.1 Prove that ΔKLM is an isosceles, right
angled triangle.
15.2 Calculate the area of ΔKLM.
P(3 ; 2), Q(−3 ; 4), R(a ; b) en S(c ; d) is die
hoekpunte van vierhoek PQRS.
16.1 Bereken die koördinate van R as T(1 ; 2) die
middelpunt van PR is.
Ant. / Ans. 16.1
16.2 Bereken die koördinate van S as PQRS 'n
parallelogram is.
Ant. / Ans. 16.2
16.3 Bewys dat PQRS 'n reghoek
is.
Ant. / Ans. 16.3
P(3 ; 2), Q(−3 ; 4), R(a ; b) and S(c ; d) are the
vertices of quadrilateral PQRS.
16.1 Caclculate the coordinates of R if T(1 ; 2) is the
midpoint of PR.
Ant. / Ans. 16.1
16.2 Calculate the coordinates of S if PQRS is
a parallelogram.
Ant. / Ans. 16.2
16.3 Prove that PQRS is a
rectangle.
Ant. / Ans. 16.3
A(−2 ; 1) en B(4 ; 16) is twee punte op
'n lyn. C en D is twee punte op die lyn met
vergelyking 5x − 2y − 14 = 0 Kan die
vierhoek ABCD 'n trapesium wees? Gee redes.
A(−2 ; 1) and B(4 ; 16) are two points on
a line. C and D are two points on the line with
equation 5x − 2y − 14 = 0. Is it possible that
quadrilateral ABCD can be a trapezium? Give reasons.
P(−4 ; 13) en Q(2 ; −2) is twee punte
op 'n lyn. Q en R is twee punte op die lyn met
vergelyking 2x − 5y − 5 = 0. Sê, met redes,
of PQ en QR twee aanliggende sye van 'n
reghoek kan wees?
P(−4 ; 13) and Q(2 ; −2) are two points on
a line. Q and R are two points on the
line 2x − 5y − 5 = 0. State, giving reasons,
whether PQ and QR can be two adjacent sides
of a rectangle?