math problem(URGENT)

Ayesha abid

Can somebody help me out with this Question?

P is the point (2,3) and Q is the point (9,5)
a) find the equation of the line joining PQ.​
b) find the coordinates of the point where the line PQ intersects the x-axis.​
c) the line y=5 is the line of symmetry of triangle PQR. find the coordinates of R.​
d) find the area of triangle PQR.​
e) calculate the length of PQ and hence calculate the perpendicular distance from R to the line PQ.​

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PlanetMaster

a) Since you have points P and Q, their equation would be in the form $$y=mx+c$$ where
$$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$
$$m=\frac{5-3}{9-2}=\frac{2}{7}$$

Substituting back into $$y=mx+c$$ and substituting x and y coordinates from either P or Q should give $$c=\frac{17}{7}$$.

Thus equation of the line joining PQ is $$y=\frac{1}{7}(2x+17)$$

b) At x-axis, y=0 so $$x=-\frac{17}{2}$$ and therefore coordinates would be $$(-\frac{17}{2},0)$$

c) You'll have to either visualize or sketch this. Since line of symmetry is y=5 and Q has coordinated (9,5), R will have same x-coordinates as P and y-coordinates would be 2(5-3)+3 so R will have coordinates (2,7).

d) We can simply use $$\frac{1}{2}\times\text{base}\times\text{height}$$ where base would be the length PR and height would be length mid-of-PR and Q (refer to your sketch). This would give the area $$14 units^{2}$$.

e) You can simple use the formula to find length between two points $$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$$

If anything is unclear, feel free to ask and I'll be happy explain in more detail.

thanks