**Question 9**:

Diagram 5 shows a rhombus

*KLMN*.

Given that

*KN*= 10 units.

Find

(a) gradient of straight line

*LM*.

(b) the equation of straight line

*MN*.

[4 marks]

**Solution**:

**(a)**

$\begin{array}{l}\text{Point}k=\left(-6,0\right)\\ {m}_{LM}={m}_{KN}\\ {m}_{LM}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ {m}_{LM}=\frac{6-0}{2-\left(-6\right)}\\ {m}_{LM}=\frac{6}{8}=\frac{3}{4}\end{array}$

**(b)**

$\begin{array}{l}KL=KN=10\text{units}\\ \therefore OL=\sqrt{K{L}^{2}-O{K}^{2}}\\ \text{}=\sqrt{{10}^{2}-{6}^{2}}\\ \text{}=\sqrt{64}\\ \text{}=8\text{units}\\ \\ {m}_{MN}={m}_{KL}\\ \text{}=-\frac{\text{y-intercept}}{\text{x-intercept}}\\ \text{}=-\frac{8}{\left(-6\right)}\\ \text{}=\frac{4}{3}\\ \\ {y}_{1}=m{x}_{1}+c\\ 6=\frac{4}{3}\left(2\right)+c\\ c=6-\frac{8}{3}\\ c=\frac{10}{3}\\ \\ \therefore \text{Equation of the straight line}MN\\ y=mx+c\\ y=\frac{4}{3}x+\frac{10}{3}\end{array}$

**Soalan 10**:

Mr. Eric and Mrs. Lisa have bought a house. They plan to buy fire insurance for their house. The insurable value of their house is RM375 000. The insurance policy chosen by them has a co-insurance provision to insure 80% of the insurable value of his home. The deductible value is RM3 200.

**(a)**Calculate the amount of insurance that they should buy for their house.

**(b)**A small fire occured in their house resulting in a loss value of RM27 500 .

Calculate the compensation payment that would be received if they insured their house on amount of insurance they would have to buy.

**(c)**If their entire house was burnt down in a fire, would they receive compensation of RM375 000 if they insure their house according to the amount in 10(a) ?

Give your justification and state the value of compensation received.

[4 marks]

**Penyelesaian**:

**(a)**

$\begin{array}{l}\text{Amount of insurance should be bought}\\ =\text{RM}375\text{}000\times \frac{80}{100}\\ =\text{RM}300\text{}000\end{array}$

**(b)**

Compensation payment

= loss value – deductible

= RM27 500 – RM3 200

= RM24 300

**(c)**

**No**, they would not receive compensation of RM375 000.

Maximum compensation will receive

= RM300 000 – RM3 200

= RM296 800

Thus, Mr. Eric and Mrs. Lisa would only receive compensation of RM296 800 because the deductible value is RM3 200.