Question 1033981
{{{drawing(400,2600/9,-9,9,-3,10,

graph(400,2600/9,-9,9,-3,10),

triangle(0,0,5,0,7,8), locate(0.8,0.89,"O(0,0)"),
locate(7,8,"B(7,8)"), locate(5.3,.89,"A(5,0)") )}}}
</pre>
a) The gradient of AB,
<pre>
{{{matrix(1,9,

matrix(1,3,gradient,of,AB),

""="", 

(matrix(1,3,"(y-coordinate",of,"B)")-matrix(1,3,"(y-coordinate",of,"A)"))/(matrix(1,3,"(x-coordinate",of,"B)")-matrix(1,3,"(x-coordinate",of,"A)")),

""="",

(8-0)/(7-5),

""="",

8/2,

""="",

4 )}}}
</pre>
b) The equation of AB,
<pre>
Let Z(x,y) be a random point on AB

{{{drawing(400,2600/9,-9,9,-3,10,
circle(6.4,5.6,0.15),circle(6.4,5.6,0.13),circle(6.4,5.6,0.11),circle(6.4,5.6,0.09),circle(6.4,5.6,0.07),circle(6.4,5.6,0.05),circle(6.4,5.6,0.03),circle(6.4,5.6,0.01),green(line(7,0,7,8)),


graph(400,2600/9,-9,9,-3,10),
locate(6.4,5.6,"Z(x,y)"),
triangle(0,0,5,0,7,8), locate(0.8,0.89,"O(0,0)"),
locate(7,8,"B(7,8)"), locate(5.3,.89,"A(5,0)") )}}}

{{{matrix(1,3,

matrix(1,3,gradient,of,AB),

""="", 

(matrix(1,3,"(y-coordinate",of,"Z)")-matrix(1,3,"(y-coordinate",of,"A)"))/(matrix(1,3,"(x-coordinate",of,"Z)")-matrix(1,3,"(x-coordinate",of,"A)")) )}}}

{{{matrix(1,3,
4,
""="",
(y-0)/(x-5)
)}}}

{{{matrix(1,3,
4/1,
""="",
y/(x-5)
)}}}

Cross-multiply:

{{{matrix(1,3,
y,
""="",
4(x-5)
)}}}

{{{matrix(1,3,
y,
""="",
4x-20
)}}}
</pre>
c) The area of &#9650; OAB,
<pre>
{{{matrix(1,7,
Area,""="",1/2,"×",base,"×",height)}}}

{{{matrix(1,5,base,""="",OA,""="",5)}}}
{{{matrix(1,7,height,""="",green,line,above,""="",8)}}}

{{{matrix(1,9,
Area,""="",1/2,"×",5,"×",8,""="",20)}}}

Edwin</pre>